Publications -- Jian-Guo Liu

Preprints:

  • D. Qi and J.-G. Liu,
    • Oscillatory solutions at the continuum limit of Lorenz 96 systems
    submitted. arXiv:2410.10073

  • Y. Gao, W. Li and J.-G. Liu,
    • Fluctuations in Wasserstein dynamics on Graphs
    submitted. arXiv:2408.08505

  • Z. Cai, J.-G. Liu, Y. Wang
    • Convergence of Random Batch Method with replacement for interacting particle systems
    submitted. arXiv:2407.19315

  • D. Qi and J.-G. Liu,
    • Coupled Stochastic-Statistical Equations for Filtering Multiscale Turbulent Systems
    submitted. arXiv:2407.04881

  • Y. Feng, Q. He, J.-G. Liu, Z. Zhou,
    • Rigorous derivation of a Hele-Shaw type model and its non-symmetric traveling wave solution
    submitted. arXiv:2404.16353

  • P. Degond and J.-G. Liu,
    • Binary particle collisions with mass exchange
    submitted. arXiv:2401.04562

  • Y. Wang, A. Gupta, D. Carpenter, T. Mullikin, Z.J. Reitman, S. Floyd, J. Kirkpatrick, J.K. Salama, P.W. Sperduto, J.-G. Liu, M.R. Bashir, K.J. Lafata,
    • A personalized Uncertainty Quantification framework for patient survival models: estimating individual uncertainty of patients with metastatic brain tumors in the absence of ground truth
    submitted. arXiv:2311.17173

  • Y. Gao, J.-G. Liu, O. Tse
    • Optimal control formulation of transition path problems for Markov Jump Processes
    submitted. arXiv:2311.07795

  • J.-G. Liu and Z. Liu,
    • Diffusion approximations of Oja's online principal component analysis
    submitted. arXiv:2301.01339

  • J.-G. Liu and Z. Liu,
    • Convergence of Oja's online principal component flow
    submitted. arXiv:2202.11308

  • J.-G. Liu and R. Pego,
    • In search of local singularities in ideal potential flows with free surface
    submitted. arXiv:2108.00445

  • Z. Zhu, J.-G. Liu, L. Li,
    • A Modified Levy Jump-Diffusion Model Based on Market Sentiment Memory for Online Jump Prediction
    submitted. arXiv:1709.03611

    2024:

  • Y. Gao, J.-G. Liu, and Z. Liu,
    • Some properties on the reversibility and the linear response theory of Langevin dynamics
    submitted arXiv:2408.13600

  • L. Li, J.-G. Liu, and Y. Wang
    • Geometric ergodicity of SGLD via reflection coupling
    Stochastics and Dynamics, arXiv:2301.06769 ,
      doi:10.1142/S0219493724500357

  • J.-G. Liu, T. Witelski, X. Xu, and Jiaqi Zhang,
    • A Three-dimensional tumor growth model and its boundary instability
    Communications on Applied Mathematics and Computation, to appear arXiv:2401.04954 ,
      doi:10.1007/s42967-024-00443-5

  • Y. Feng, L. Li, J.-G. Liu, T. Tang,
    • Some Gronwall inequalities for a class of discretizations of time fractional equations on nonuniform meshes
    SIAM J. Numer. Anal., 62 (2024) 2196-2221. PDF file ,
      doi:10.1137/24M1631614

  • J.-G. Liu and R.L. Pego,
    • A simple construction of fat Cantor sets
    American Mathematical Monthly, 131 (2024) 525. PDF file ,
      doi: 10.1080/00029890.2024.2322909

  • V. Cherepanov, J.-G. Liu, Z. Qian,
    • On the dynamics of the boundary vorticity for incompressible viscous flows
    Journal of Scientific Computing, 99 (2024) 24 PDF file ,
      doi: 10.1007/s10915-024-02498-1

  • Y. Gao, W. Li and J.-G. Liu,
    • Master equations for finite state mean field games with nonlinear activations
    Discrete and Continuous Dynamical Systems Series B, 29 (2024) 2837-2879. PDF file ,
      doi: 10.3934/dcdsb.2023204

  • Y. Feng, L. Li, J.-G. Liu, X. Xu,
    • Existence of weak solutions to p-Navier-Stokes equations
    Discrete and Continuous Dynamical Systems Series B, 29 (2024) 1868-1890. PDF file ,
      doi: 10.3934/dcdsb.2023159

  • J.-G. Liu and J. Wang,
    • The best constant for L∞-type Gagliardo-Nirenberg inequalities
    Quarterly of Applied Mathematics, 82 (2024) 305-338. PDF file ,
      doi: 10.1090/qam/1645

  • J.B Stevens, B.A Riley, J. Je, Y. Gao, C. Wang, Y.M Mowery, D.M Brizel, F.‐F. Yin, J.‐G. Liu, and K.J Lafata
    • Radiomics on spatial‐temporal manifolds via Fokker‐Planck dynamics
    Medical Physics 51 (2024) 3334-3347. PDF file ,
      doi: 10.1002/mp.16905



    2023:

  • Y. Gao and J.-G. Liu,
    • A selection principle for weak KAM solutions via Freidlin-Wentzell large deviation principle of invariant measures
    SIAM J. Math. Anal. 55 (2023) 6457-6495 PDF file ,
      doi: 10.1137/22M1519717

  • Y. Gao and J.-G. Liu
    • Book review "Stochastic Chemical Reaction Systems in Biology. By Hong Qian and Hao Ge"
    SIAM Review, 65 (2023) 539-540. PDF file ,
      doi: 10.1137/23N975715

  • Y. Gao and J.-G. Liu,
    • Large deviation principle and thermodynamic limit of chemical master equation via nonlinear semigroup
    Multiscale Model. Simul., 21 (2023) 1534--1569 PDF file ,
      doi: 10.1137/22M1505633

  • D. Qi and J.-G. Liu,
    • High-order Moment Closure Models with Random Batch Method for Efficient Computation of Multiscale Turbulent Systems
    Chaos, 33 (2023) 103133 PDF file ,
      doi: 10.1063/5.0160057

  • Y. Gao and J.-G. Liu,
    • Random walk approximation for irreversible drift-diffusion process on manifold: ergodicity, unconditional stability and convergence
    Commun. Comput. Phys. 34 (2023) 132-172 PDF file ,
      doi: 10.4208/cicp.OA-2023-0021

  • D. Qi and J.-G. Liu,
    • A random batch method for efficient ensemble forecasts of multiscale turbulent systems
    Chaos, 33 (2023) 023113 PDF file ,
      doi: 10.1063/5.0129127

  • J.-G. Liu, Y. Tang, Y. Zhao,
    • On the equilibrium of the Poisson-Nernst-Planck-Bikermann model equipping with the steric and correlation effects
    Comm Math Sci, 21 (2023) 485-515. PDF file ,
      doi: 10.4310/CMS.2023.v21.n2.a8

  • Y. Gao, T. Li, X. Li, J.-G. Liu
    • Transition path theory for Langevin dynamics on manifolds: optimal control and data-driven solver
    Multiscale Model. Simul, 21 (2023) 1-33 PDF file ,
      doi: 10.1137/21M1437883

  • Y. Wang, X. Li, M. Konanur, B. Konkel, E. Seyferth, N. Brajer, J.-G. Liu, M. Bashir, K.J. Lafata,
    • Deep fusion of CT imaging and blood markers to estimate portal venous hypertension: novel optimization of data fusion quality
    Medical Physics, (2023) 1-12 PDF file ,
      doi: 10.1002/mp.16181

  • X. Dou, J.-G. Liu, Z. Zhou,
    • A tumor growth model with autophagy: The reaction-(cross-)diffusion system and its free boundary limit,
    Discrete Contin. Dyn. Syst. Ser. B, 23 (2023) 1964-1992. PDF file ,
      doi: 10.3934/dcdsb.2022154

  • Y. Gao, J.-G. Liu, N. Wu,
    • Data-driven efficient solvers for Langevin dynamics on manifold in high dimensions
    Applied and Computational Harmonic Analysis 62 (2023) 261-309. PDF file ,
      doi: 10.1016/j.acha.2022.09.003

    2022:

  • K. Craig, J.-G. Liu, J. Lu, J.L. Marzuola, L. Wang,
    • A Proximal-Gradient Algorithm for Crystal Surface Evolution,
    Numerische Mathematik 152 (2022) 631-662 PDF file ,
      doi: 10.1007/s00211-022-01320-0

  • Y. Gao and J.-G. Liu,
    • Revisit of macroscopic dynamics for some non-equilibrium chemical reactions from a Hamiltonian viewpoint
    J. Stat. Phys. 189 (2022) 22 PDF file ,
      doi: 10.1007/s10955-022-02985-5

  • L. Li, J.-G. Liu, Y. Tang,
    • Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations
    Commun. Comput. Phys., 32 (2022), 41-82. PDF file ,
      doi:10.4208/cicp.OA-2021-0159

  • L. Li, J.-G. Liu, Z. Liu, Y. Yang, and Z. Zhou,
    • On Energy Stable Runge-Kutta Methods for the Water Wave Equation and its Simplified Non-Local Hyperbolic Model
    Commun. Comput. Phys., 32 (2022), 222-258. PDF file ,
      doi:10.4208/cicp.OA-2021-0049

  • P. Degond, A. Frouvelle, and J.-G. Liu,
    • From kinetic to fluid models of liquid crystals by the moment method
    Kinetic & Related Models 15 (2022) 417-465. PDF file ,
      doi:10.3934/krm.2021047

  • Yuan Gao, Jian-Guo Liu,
    • Projection method for droplet dynamics on groove-textured surface with merging and splitting
    SIAM J. Sci. Comput. 44 (2022) B310-B338 PDF file ,
      doi:10.1137/20M1338563

  • J.-G. Liu, Z. Wang, Y. Zhang, Z. Zhou,
    • Rigorous justification of the Fokker-Planck equations of neural networks based on an iteration perspective,
    SIAM J. Math. Anal. 54 (2022) 1270-1312. PDF file ,
      doi:10.1137/20M1338368

  • J.-G. Liu and Z. Zhang,
    • Existence of global weak solutions of p-Navier-Stokes equations
    Discrete Contin. Dyn. Syst. Ser. B, 27 (2022) 469-486. PDF file,
      doi:10.3934/dcdsb.2021051

    2021:

  • Y. Gao, A.E. Katsevich, J.-G. Liu, J. Lu, J.L. Marzuola
    • Analysis of a fourth order exponential PDE arising from a crystal surface jump process with Metropolis-type transition rates
    Pure and Applied Analysis 3 (2021) 595--612. PDF file ,
      doi:10.2140/paa.2021.3.595

  • J.-G. Liu, Z Wang, Y Xie, Y Zhang, and Z Zhou,
    • Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective
    Math. Neuro. and Appl., 1 (2021) article no. 2, 1--36 PDF file ,
      doi:10.46298/mna.7203

  • Y Gao and J.-G. Liu,
    • Surfactant-dependent contact line dynamics and droplet adhesion on textured substrates: derivations and computations
    Physica D, 428 (2021) 133067. PDF file ,
      doi:10.1016/j.physd.2021.133067

  • Y. Gao, J.-G. Liu, Z. Liu,
    • Existence and rigidity of the Peierls-Nabarro model for dislocations in high dimensions,
    Nonlinearity, 34 (2021) 7778-7828. PDF file ,
      doi:10.1088/1361-6544/ac24e3

  • J.-G. Liu and X Xu
    • Existence and incompressible limit of a tissue growth model with autophagy
    SIAM J. Math. Anal. 53 (2021) 5215-5242, PDF file
      doi:10.1137/21M1405253

  • Y. Gao, G. Jin, J.-G. Liu,
    • Inbetweening auto-animation via Fokker-Planck dynamics and thresholding,
    Inverse Problems and Imaging, 15 (2021) 843-864 PDF file ,
      doi:10.3934/ipi.2021016

  • K. Lafata, Y. Chang, C. Wang, Y. Mowery, I. Vergalasova, D. Niedzwiecki, D. Yoo, J.-G. Liu, D. Brizel, F.-F. Yin,
    • Intrinsic radiomic expression patterns after 20 Gy demonstrate early metabolic response of oropharyngeal cancers,
    Medical Physics. 48 (2021) 3767-3777. PDF file ,
      doi:10.1002/mp.14926

  • J.-G. Liu, J. Wang, Z. Zhou, Y. Zhao
    • Field Model for Complex Ionic Fluids: Analytical Properties and Numerical Investigation
    Commun. Comput. Phys. 30 (2021) 874-902. PDF file ,
      doi:10.4208/cicp.OA-2019-0223

  • J.-G. Liu, M. Tang, L. Wang, and Z. Zhou,
    • Towards understanding the boundary propagation speeds in tumor growth models,
    SIAM Journal on Applied Mathematics, 81 (2021) 1052-1076. PDF file ,
      doi:10.1137/19M1296665

  • Yuan Gao, Jian-Guo Liu,
    • Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface
    Interfaces Free Boundaries, 23 (2021) 103-158. PDF file ,
      doi:10.4171/IFB/451

  • S. Jin, L. Li and J.-G. Liu,
    • Convergence of the Random Batch Method for interacting particles with disparate species and weights
    SINUM, 59 (2021) 746-768. PDF file ,
      doi:10.1137/20M1327641

  • Y. Gao, J.-G. Liu, T. Luo, Y. Xiang,
    • Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space
    Discrete Contin. Dyn. Syst. Ser. B, 26 (2021) 3177-3207 PDF file ,
      doi:10.3934/dcdsb.2020224

  • J. Hu, J.-G. Liu, Y. Xie, Z. Zhou
    • A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration
    Journal of Computational Physics 433 (2021), 110195 PDF file ,
      doi:10.1016/j.jcp.2021.110195

  • Yu Gao, Yuan Gao and J.-G. Liu,
    • Large time behavior, bi-Hamiltonian structure and kinetic formulation for complex Burgers equation
    Quart. Appl. Math., 79 (2021) 55-102 PDF file ,
      doi:10.1090/qam/1573

    2020:

  • Q. Li, J.-G. Liu, R. Shu,
    • Sensitivity analysis of Burgers' equation with shocks
    SIAM/ASA J. Uncertainty Quantification 8 (2020) 1493-1521. PDF file ,
      doi:10.1137/18M1211763

  • J.-G. Liu and X. Xu,
    • On a class of functional inequalities and their applications to forth-order nonlinear parabolic equations,
    Comm Math Sci, 18 (2020) 1911-1948. PDF file ,
      doi:10.4310/CMS.2020.v18.n7.a5

  • Hui Huang, Jian-Guo Liu, Peter Pickl
    • On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system
    J. Stat. Phys. 181 (2020) 1915-1965 PDF file ,
      doi:10.1007/s10955-020-02648-3

  • J.-G. Liu and J. Wang,
    • Global existence for Nernst-Planck-Navier-Stokes system in R^n,
    Comm Math Sci. 18 (2020) 1743-1754 PDF file ,
      doi:10.4310/CMS.2020.v18.n6.a9

  • Y. Gao, J.-G. Liu,
    • A note for parametric Bayesian inference via several gradient flows.
    Annals of Mathematical Sciences and Applications, 5 (2020) 261--282. PDF file ,
      doi:10.4310/AMSA.2020.v5.n2.a3

  • Y. Gao and J.-G. Liu,
    • Long time behavior of dynamic solution to Peierls--Nabarro dislocation model
    Methods and Applications of Analysis, 27 (2020) 161-198. PDF file ,
      doi:10.4310/MAA.2020.v27.n2.a4

  • Y. Gao, J.-G. Liu, J. Lu, J.L. Marzuola,
    • Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects,
    Nonlinearity 33 (2020) 3816-3845. PDF file ,
      doi:10.1088/1361-6544/ab853d

  • L. Li, Y. Li, J.-G Liu, Z. Liu, J. Lu,
    • A stochastic version of Stein variational gradient descent for efficient sampling
    Comm App Math Comp Sci, 15 (2020) 37-63. PDF file ,
      doi:10.2140/camcos.2020.15.37

  • L. Li, J.-G. Liu,
    • Large time behaviors of upwind schemes and B-schemes for Fokker-Planck equations on R by jump processes,
    Math Comp, 89 (2020) 2283-2320. PDF file ,
      doi:10.1090/mcom/3516

  • Y. Feng, T. Gao, L. Li, J.-G. Liu, Y. Lu,
    • Uniform-in-time weak error analysis for stochastic gradient descent algorithms via diffusion approximation
    Comm. Math. Sci., 18 (2020) 163-188. PDF file ,
      doi:10.4310/CMS.2020.v18.n1.a7

  • P. Degond, M. Engel, J.-G. Liu, and R.L. Pego,
    • A Markov jump process modelling animal group size statistics
    Comm Math Sci, 18 (2020) 55-89. PDF file ,
      doi:10.4310/CMS.2020.v18.n1.a3

  • S. Jin, L. Li, J.-G. Liu,
    • Random batch methods (RBM) for interacting particle systems
    J. Comput. Phy, 400 (2020) 108877. PDF file ,
      doi:10.1016/j.jcp.2019.108877

    2019:

  • J-G Liu and R Yang,
    • Propagation of Chaos for the Keller-Segel Equation with a Logarithmic Cut-off,
    Methods and Applications of Analysis, 26 (2019) 319-348. PDF file ,
      doi:10.4310/MAA.2019.v26.n4.a2

  • J.-G. Liu and R. Pego,
    • On local singularities in ideal potential flows with free surface,
    Chin. Ann. Math, 40 (2019) 925-948. PDF file ,
      doi:10.1007/s11401-019-0167-z

  • J.-G. Liu, R.L. Pego, Y. Pu,
    • Well-posedness and derivative blow-up for a dispersionless regularized shallow water system,
    Nonlinearity, 32 (2019) 4346. PDF file ,
      doi:10.1088/1361-6544/ab2cf1

  • L. Li, J.-G. Liu, P. Yu
    • On mean field limit for Brownian particles with Coulomb interaction in 3D,
    J. Math. Phys. 60 , (2019) 111501. PDF file ,
      doi:10.1063/1.5114854

  • A. Liu, J.-G. Liu and Y. Lu,
    • On the rate of convergence of empirical measure in infinity-Wasserstein distance for unbounded density function
    Quart. Appl. Math., 77 (2019) 811-829. PDF file ,
      doi:10.1090/qam/1541

  • Y. Gao, J.-G. Liu, and X.Y. Lu,
    • Gradient flow approach to an exponential thin film equation: global existence and latent singularity
    ESAIM Control Optim. Calc. Var., 25 (2019) 49. PDF file ,
      doi:10.1051/cocv/2018037

  • J.-G. Liu, R.L. Pego and D. Slepčev,
    • Least action principles for incompressible flows and geodesics between shapes
    Calc Var Partial Differ Equ, 58 (2019) 179. PDF file ,
      doi:10.1007/s00526-019-1636-7

  • L. Li, J.-G. Liu
    • A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows,
    SIAM J. Numer. Anal., 57 (2019) 2095-2120. PDF file ,
      doi:10.1137/19M123854X

  • Q. Zhan, M. Zhuang, Z. Zhou, J.-G. Liu, and Q.H. Liu,
    • Complete-Q Model for Poro-Viscoelastic Media in Subsurface Sensing: Large-Scale Simulation With an Adaptive DG Algorithm,
    IEEE Trans. Geosci. Remote Sens. 57 (2019) 4591--4599. PDF file ,
      doi:10.1109/tgrs.2019.2891691

  • K. Lafata, Z. Zhou, J.-G. Liu, J. Hong, C. Kelsey, and F.-F. Yin,
    • An Exploratory Radiomics Approach to Quantifying Pulmonary Function in CT Images,
    Sci. Rep., (2019) 9:11509 PDF file ,
      doi:10.1038/s41598-019-48023-5

  • A Frouvelle, J.G. Liu,
    • Long-time dynamics for a simple aggregation equation on the sphere
    in "IHPStochDyn 2017: Stochastic Dynamics Out of Equilibrium", edited by G. Giacomin, S Olla, E Saada, H Spohn, and G Stoltz, Springer (2019), pp 457-482.. PDF file ,
      doi:10.1007/978-3-030-15096-9_16

  • J.-G. Liu, B. Niethammer, and R. Pego,
    • Self-similar spreading in a merging-splitting model of animal group size
    J. Stat Phys, 175 (2019) 1311-1330. PDF file ,
      doi:10.1007/s10955-019-02280-w

  • J.-G. Liu, J. Lu, D. Margetis and J.L. Marzuola,
    • Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model
    Physica D, 393 (2019) 54-67. pdf file ,
      doi:10.1016/j.physd.2019.01.004

  • K. Lafata, Z. Zhou, J.-G. Liu, F.F. Yin,
    • Data clustering based on Langevin annealing with a self-consistent potential.
    Quart. Appl. Math., 77 (2019) 591-613 pdf file ,
      doi:10.1090/qam/1521

  • J.-G. Liu, M. Tang, L. Wang, and Z. Zhou,
    • Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamics
    Discrete Contin. Dyn. Syst. Ser. B, 24 (2019)3011-3035. PDF file ,
      doi:10.3934/dcdsb.2018297

  • MV de Hoop, J.-G. Liu, P.A. Markowich, N.S. Ussembayev
    • Plane-wave analysis of a hyperbolic system of equations with relaxation in
    Comm Math Sci, 17 (2019) 61-79. PDF file ,
      doi:10.4310/cms.2019.v17.n1.a3

  • J.-G. Liu and R.M. Strain,
    • Global stability for solutions to the exponential PDE describing epitaxial growth
    Interfaces Free Boundaries, 21 (2019) 51-86, PDF file ,
      doi:10.4171/IFB/417

  • Q. Zhan, M. Zhuang, Y. Fang, J.-G. Liu, and Q.H. Liu,
    • Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization
    Proc. R. Soc. A, 475 (2019) 20180610 PDF file ,
      doi:10.1098/rspa.2018.0610

  • Y. Gao, L. Li and J.-G. Liu,
    • Patched peakon weak solutions of the modified Camassa-Holm equation
    Physica D, 390 (2019) 15-35. PDF file ,
      doi:10.1016/j.physd.2018.10.005

  • W. Hu, C.J. Li, L. Li, and J.-G. Liu,
    • On the diffusion approximation of nonconvex stochastic gradient descent,
    Annals of Mathematical Sciences and Applications, 4 (2019) 3-32. PDF file ,
      doi:10.4310/amsa.2019.v4.n1.a1

  • Hui Huang, Jian-Guo Liu, and Jianfeng Lu
    • Learning interacting particle systems: diffusion parameter estimation for aggregation equations
    Math. Models Methods Appl. Sci., 29 (2019) 1-29 PDF file ,
      doi:10.1142/S0218202519500015

  • K. Lafata, J. Hong, R. Geng, B. Ackerson, J.-G. Liu, Z. Zhou, J. Torok, C. Kelsey, F.-F. Yin
    • Association of Pre-treatment Radiomic Features with Lung Cancer Recurrence Following Stereotactic Body Radiation Therapy
    Phys. Med. Biol. 64 (2019) 025007. pdf file ,
      doi:10.1088/1361-6560/aaf5a5

    2018:

  • L. Li and J.-G. Liu,
    • Some compactness criteria for weak solutions of time fractional PDEs
    SIAM J. Math. Anal., 50 (2018) 3963-3995. pdf file ,
      doi:10.1137/17M1145549

  • Y. Gao, H. Ji, J.-G. Liu, T.P. Witelski,
    • A vicinal surface model for epitaxial growth with logarithmic free energy
    Discrete Contin. Dyn. Syst. Ser. B, 23 (2018) 4433-4453. pdf file ,
      doi:10.3934/dcdsb.2018170

  • Y. Feng, L. Li and J.-G. Liu,
    • Semigroups of stochastic gradient descent and online principle component analysis: properties and diffusion approximations.
    Comm. Math. Sci., 16 (2018) 777-789. pdf file ,
      doi:10.4310/CMS.2018.v16.n3.a8

  • Y. Gao and J.-G. Liu,
    • The modified Camassa-Holm equation in Lagrangian coordinates
    Discrete Contin. Dyn. Syst. Ser. B, 23 (2018) 2545-2592. pdf file ,
      doi:10.3934/dcdsb.2018067

  • Y. Feng, L. Li, J.-G. Liu and X. Xu,
    • Continuous and discrete one dimensional autonomous fractional ODEs
    Discrete Contin. Dyn. Syst. Ser. B, 23 (2018) 3109-3135. pdf file ,
      doi:10.3934/dcdsb.2017210

  • Y. Gao, L. Li and J.-G. Liu,
    • A dispersive regularization for the modified Camassa-Holm equation
    SIAM J. Math Anal, 50 (2018) 2807-2838. pdf file ,
      doi:10.1137/17M1132756

  • L. Li and J.-G. Liu,
    • A generalized definition of Caputo derivatives and its application to fractional ODEs
    SIAM J. Math Anal, 50 (2018) 2867-2900. pdf file ,
      doi:10.1137/17M1160318

  • K. Chen, Q. Li, and J.-G. Liu,
    • Online learning in optical tomography: a stochastic approach
    Inverse Probl, 34 (2018) 075010. pdf file ,
      doi:10.1088/1361-6420/aac220

  • J.-G. Liu, M. Tang, L. Wang, and Z. Zhou,
    • An accurate front capturing scheme for tumor growth models with a free boundary limit
    J. Comput. Phy, 364 (2018) 73-94. pdf file ,
      doi:10.1016/j.jcp.2018.03.013

  • L. Li, J.-G. Liu, and L. Wang,
    • Cauchy problems for Keller-Segel type time-space fractional diffusion equation
    J. Diff. Eqs, 265 (2018) 1044-1096. pdf file ,
      doi:10.1016/j.jde.2018.03.025

  • L. Li and J.-G. Liu,
    • p-Euler equations and p-Navier-Stokes equations,
    J. Diff. Eqs, 264 (2018) 4707-4748. pdf file ,
      doi:10.1016/j.jde.2017.12.023

  • Y. Gao, J.-G. Liu, X.-Y. Lu, and X. Xu,
    • Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface
    Calc Var Partial Differ Equ, (2018) 57:55. pdf file ,
      doi:10.1007/s00526-018-1326-x

  • J.-G. Liu and X. Xu,
    • Partial regularity for weak solutions to a PDE system with cubic nonlinearities,
    J. Diff. Eqs, 264 (2018) 5489-5526. pdf file ,
      doi:10.1016/j.jde.2018.01.001

  • Y. Feng, L. Li, J.-G. Liu and X. Xu,
    • A note on one-dimensional time fractional ODEs,
    Appl. Math. Lett, 83 (2018) 87-94. pdf file ,
      doi:10.1016/j.aml.2018.03.015

  • J.-G. Liu, L. Wang, and Z. Zhou,
    • Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations,
    Math. Comp., 87 (2018) 1165-1189. pdf file ,
      doi:10.1090/mcom/3250

  • F. Coquel, S. Jin, J.-G. Liu and L. Wang,
    • Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar hyperbolic conservation laws,
    Math. Comp., 87 (2018) 1083-1126 pdf file ,
      doi:10.1090/mcom/3253

  • L. Li and J.-G. Liu,
    • A note on deconvolution with completely monotone sequences and discrete fractional calculus
    Quart. Appl. Math., 76 (2018) 189--198. pdf file ,
      doi:10.1090/qam/1479

    2017:

  • H. Huang and J.-G. Liu,
    • Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis
    Comm. Math. Sci., 15 (2017) 1821--1842. pdf file ,
      doi:10.4310/CMS.2017.v15.n7.a2

  • L. Li, J.-G. Liu and J. Lu,
    • Fractional stochastic differential equations satisfying fluctuation-dissipation theorem,
    J Stat Phys, 169 (2017) 316--339. pdf file ,
      doi:10.1007/s10955-017-1866-z

  • Y. Gao, H. Ji, J.-G. Liu, T.P. Witelski,
    • Global existence of solutions to a tear film model with locally elevated evaporation rates
    Physica D, 350 (2017) 13--25. pdf file ,
      doi:10.1016/j.physd.2017.03.005

  • J.-G. Liu and X. Xu,
    • Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions,
    SIAM J. Math Anal, 49 (2017) 2220-2245. pdf file ,
      doi:10.1137/16M1098474

  • P. Degond, M. Herty, J.-G. Liu,
    • Meanfield games and model predictive control
    Comm Math Sci, 15 (2017) 1403--1422. pdf file ,
      doi:10.4310/CMS.2017.v15.n5.a9

  • S. Jin, J.-G. Liu and Z. Ma,
    • Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro-macro decomposition-based asymptotic-preserving method
    Research in the Mathematical Sciences, (2017) 4:15. pdf file ,
      doi:10.1186/s40687-017-0105-1

  • Y. Gao, J.-G. Liu, J. Lu,
    • Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime
    SIAM J. Math Anal, 49 (2017) 1705--1731. pdf file ,
      doi:10.1137/16M1094543

  • J.-G. Liu, Z. Ma and Z. Zhou,
    • Explicit and implicit TVD schemes for conservation laws with Caputo derivatives,
    J. Sci. Comput., 72 (2017) 291--313. pdf file ,
      doi:10.1007/s10915-017-0356-4

  • H. Huang and J.-G. Liu,
    • Error estimate of a random particle blob method for the Keller-Segel equation
    Math. Comp., 86 (2017) 2719--2744. pdf file ,
      doi:10.1090/mcom/3174

  • Y. Gao, J.-G. Liu, J. Lu,
    • Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces
    J. Nonlinear Sci, 27 (2017), 873--926. pdf file ,
      doi:10.1007/s00332-016-9354-1

  • Y. Gao and J.-G. Liu,
    • Global convergence of sticky particle method for modified Camassa-Holm equation,
    SIAM J. Math Anal, 49 (2017) 1267--1294. pdf file ,
      doi:10.1137/16M1102069

  • P. Degond, J.-G. Liu, and R.L. Pego
    • Coagulation-fragmentation model for animal group-size statistics
    J. Nonlinear Sci, 27 (2017) 379--424. pdf file ,
      doi:10.1007/s00332-016-9336-3

  • J.-G. Liu and J. Wang,
    • Global existence for a thin film equation with subcritical mass,
    Discrete Contin. Dyn. Syst. Ser. B, 22 (2017) 1461-1492. pdf file ,
      doi:10.3934/dcdsb.2017070

  • P. Degond, J.-G. Liu, S. Merino-Aceituno, T. Tardiveau,
    • Continuum dynamics of the intention field under weakly cohesive social interactions
    Math. Models Methods Appl. Sci., 27 (2017) 159--182. pdf file ,
      doi:10.1142/S021820251740005X

  • J.-G. Liu and R. Yang,
    • A random particle blob method for the Keller-Segel equation and convergence analysis
    Math. Comp., 86 (2017) 725--745. pdf file ,
      doi:10.1090/mcom/3118

  • W. Cong and J.-G. Liu,
    • Uniform $L^{\infty}$ boundedness for a degenerate parabolic-parabolic Keller-Segel model,
    Discrete Contin. Dyn. Syst. Ser. B, 22 (2017) 307--338. pdf file ,
      doi:10.3934/dcdsb.2017015

  • J.-G. Liu and J. Wang,
    • A generalized Sz. Nagy inequality in higher dimensions and the critical thin film equation,
    Nonlinearity 30 (2017) 35 -- 60. pdf file ,
      doi:10.1088/0951-7715/30/1/35

    2016:

  • J.-G. Liu and X. Xu
    • Existence theorems for a multi-dimensional crystal surface model
    SIAM J. Math Anal, 48 (2016) 3667--3687. pdf file ,
      doi:10.1137/16M1059400

  • H. Huang and J.-G. Liu,
    • Error estimates of the aggregation-diffusion splitting algorithms for the keller-segel equations,
    Discrete Contin. Dyn. Syst. Ser. B, 21 (2016) 3463--3478. pdf file ,
      doi:10.3934/dcdsb.2016107

  • J.-G. Liu and R. Yang,
    • Propagation of chaos for large Brownian particle system with Coulomb interaction
    Research in the Mathematical Sciences, (2016) 3:40. pdf file ,
      doi:10.1186/s40687-016-0086-5

  • J. Chen, J.-G. Liu and Z. Zhou,
    • On a Schrodinger-Landau-Lifshitz system: Variational structure and numerical methods
    Multiscale Model. Simul, 14 (2016) 1463-1487. pdf file ,
      doi:10.1137/16M106947X

  • J.-G. Liu and R.L. Pego
    • On generating functions of Hausdorff moment sequences
    Trans. Amer. Math. Soc. 368 (2016) 8499-8518 pdf file ,
      doi:10.1090/tran/6618

  • W. Cong and J.-G. Liu,
    • A degenerate p-Laplacian Keller-Segel model
    Kinetic & Related Models, 9 (2016) 687--714. pdf file ,
      doi:10.3934/krm.2016012

  • H. Huang and J.-G. Liu,
    • Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos
    Kinetic & Related Models, 9 (2016) 715--748. pdf file ,
      doi:10.3934/krm.2016013

  • J.-G. Liu and Y. Zhang,
    • Convergence of diffusion-drift many particle systems in probability under a Sobolev norm
    in "From Particle Systems to Partial Differential Equations III", edited by P. Goncalves and A.J. Soares, Ana Jacinta, Springer, (2016), pp. 195-224. pdf file ,
      doi:10.1007/978-3-319-32144-8_10

  • J.-G. Liu and Y. Zhang,
    • Convergence of stochastic interacting particle systems in probability under a Sobolev norm
    Annals of Mathematical Sciences and Applications, 1 (2016) 251--299. pdf file ,
      doi:10.4310/AMSA.2016.v1.n2.a1

  • H. Huang and J.-G. Liu,
    • A note on Monge-Ampere Keller-Segel equation
    Appl Math Lett, 61 (2016) 26-34 pdf file ,
      doi:10.1016/j.aml.2016.05.003

  • Y. Duan and J.-G. Liu,
    • Error estimate of the particle method for the b-equation
    Methods and Applications of Analysis, 23 (2016) 119--154. pdf file ,
      doi:10.4310/MAA.2016.v23.n2.a1

  • G.J. Herschlag, J.-G. Liu, A.T. Layton,
    • Fluid extraction across pumping and permeable walls in the viscous limit
    Phys. Fluids, 28 (2016), 041902 pdf file ,
      doi:10.1063/1.4946005

  • J.-G. Liu and J. Wang,
    • A note on $L^{\infty}$-bound and uniqueness to a degenerate Keller-Segel model
    Acta Appl. Math., 142 (2016) 173--188. pdf file ,
      doi:10.1007/s10440-015-0022-5

  • J.-G. Liu and J. Wang,
    • Refined hyper-contractivity and uniqueness for the Keller-Segel equations
    Appl Math Lett, 52 (2016) 212-219 pdf file ,
      doi:10.1016/j.aml.2015.09.001

    2015:

  • G.J. Herschlag, J.-G. Liu, A.T. Layton,
    • An exact solution for Stokes flow in a channel with arbitrarily large wall permeability
    SIAM J Appl Math, 75 (2015) 2246-2267 pdf file ,
      doi:10.1137/140995854

  • Y. Xue, C. Wang and J.-G. Liu,
    • Simple finite element numerical simulation of incompressible flow over non-rectangular domains and the super-convergence analysis
    J. Sci. Comput., 65 (2015) 1189-1216 pdf file ,
      doi:10.1007/s10915-015-0005-8

  • A. Chertock, J.-G. Liu, and T. Pendleton
    • Elastic collisions among peakon solutions for the Camassa-Holm equation
    Appl. Numer. Math., 93 (2015) 30-46 pdf file ,
      doi:10.1016/j.apnum.2014.01.001

  • J. Lu, J.-G. Liu and D. Margetis,
    • Emergence of step flow from atomistic scheme of epitaxial growth in 1+1 dimensions
    Phys. Rev. E, 91 (2015) 032403 pdf file ,
      doi:10.1103/PhysRevE.91.032403

  • P. Degond, A. Frouvelle, J.-G. Liu
    • Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics
    Arch. Rat. Mech. Anal. 216 (2015) 63-115 pdf file ,
      doi:10.1007/s00205-014-0800-7

    2014:

  • F. Coquel, S. Jin, J.-G. Liu and L. Wang,
    • Well-posedness and singular limit of a semilinear hyperbolic relaxation system with a two-scale discontinuous relaxation rate,
    Arch. Rat. Mech. Anal. 214 (2014) 1051-1084. PDF file ,
      doi:10.1007/s00205-014-0773-6

  • P. Degond, J.-G. Liu and C. Ringhofer,
    • Evolution of wealth in a nonconservative economy driven by local Nash equilibria
    Phil. Trans. R. Soc. A 372 (2014) 20130394 PDF file ,
      doi:10.1098/rsta.2013.0394

  • X. Chen, A. Jungel, J.-G. Liu
    • A note on Aubin-Lions-Dubinskii lemmas
    Acta Appl. Math., 133 (2014) 33-43 PDF file ,
      doi:10.1007/s10440-013-9858-8

  • H. Johnston, C. Wang and J.-G. Liu,
    • A local pressure boundary condition spectral collocation scheme for the three-dimensional Navier-Stokes equations,
    J. Sci. Comput., 60 (2014) 612-626. PDF file ,
      doi:10.1007/s10915-013-9808-7

  • X. Chen, X. Liu and J.-G. Liu,
    • Existence and uniqueness of global weak solution to a kinetic model for the sedimentation of rod-like particles
    Comm. Math. Sci., 12 (2014) 1579-1601. PDF file ,
      doi:10.4310/CMS.2014.v12.n8.a10

  • D. Chae, P. Degond, J.-G. Liu,
    • Well-posedness for Hall-magnetohydrodynamics,
    Ann. I. H. Poincare, AN., 31 (2014) 555-565. pdf file ,
      doi:10.1016/j.anihpc.2013.04.006

  • P. Degond, A. Frouvelle, J.-G. Liu
    • A note on phase transitions for the Smoluchowski equation with dipolar potential,
    "Proceedings of the Fourteenth International Conference on Hyperbolic Problems: Theory, Numerics and Application", AIMS on Applied Mathemathics vol 8, (2014) pp 179--192, arXiv:1212.3920

  • P. Degond, M. Herty and J.-G. Liu,
    • Flow on sweeping networks
    Multiscale Model. Simul. 12 (2014) 538--565. PDF file ,
      doi:10.1137/130927061

  • T. Goudon, S. Jin, J.-G. Liu and B. Yan,
    • Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density,
    Int J Numer Methods Fluids, 75 (2014) 81-154. PDF file ,
      doi:10.1002/fld.3885

  • P. Degond, J.-G. Liu and C. Ringhofer,
    • Evolution of the distribution of wealth in an economic environment driven by local Nash equilibria
    J. Stat. Phys. 154 (2014) 751-780. PDF file ,
      doi:10.1007/s10955-013-0888-4

  • P. Degond, J.-G. Liu and C. Ringhofer,
    • Large-scale dynamics of Mean-Field Games driven by local Nash equilibria
    J Nonlinear Sci., 24 (2014) 93-115. PDF file ,
      doi:10.1007/s00332-013-9185-2

  • S. Bian, J.-G. Liu, and C. Zou,
    • Ultra-contractivity for Keller-Segel model with diffusion exponent m>1-2/d
    Kinetic & Related Models, 7 (2014) 9-28. PDF file ,
      doi:10.3934/krm.2014.7.9

  • Y. Duan and J.-G. Liu,
    • Convergence analysis of the vortex blob method for the b-equation
    Discrete Contin. Dyn. Syst. Ser. A, 34 (2014) 1995-2011. PDF file ,
      doi:10.3934/dcds.2014.34.1995

    2013:

  • S. Bian and J.-G. Liu,
    • Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent m > 0
    Comm Math Phy, 323 (2013) 1017-1070. PDF file ,
      doi:10.1007/s00220-013-1777-z

  • P. Degond, J.-G, Liu, S. Motsch, V. Panferov
    • Hydrodynamic models of self-organized dynamics: derivation and existence theory
    Methods and Applications of Analysis 20 (2013) 89-114. PDF file ,
      doi:10.4310/MAA.2013.v20.n2.a1

  • Y.L. Huang, J.-G. Liu and W.-C. Wang,
    • A generalized MAC scheme on curvilinear domains
    SIAM J. Sci. Comput. 35 (2013), B953-B986 PDF file ,
      doi:10.1137/120875508

  • P. Degond, A. Frouvelle, J.-G. Liu, S Motsch, L Navoret,
    • Macroscopic models of collective motion and self-organization
    Seminaire Laurent Schwartz -- EDP et applicatios, (2012 - 2013) , Exp. No. I, 1--27. PDF file ,
      doi:10.5802/slsedp.32

  • X. Chen and J.-G. Liu,
    • Analysis of polymeric flow models and related compactness theorems in weighted spaces
    SIAM J Math Anal, 45 (2013) 1179-1215. PDF file ,
      doi:10.1137/120887850

  • T. Goudon, S. Jin, J.-G. Liu and B. Yan,
    • Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows
    J. Comput Phy, 246 (2013) 145-164. PDF file ,
      doi:10.1016/j.jcp.2013.03.038

  • P. Degond, A. Frouvell, J.-G. Liu
    • Macroscopic limits and phase transition in a system of self-propelled particles
    J Nonlinear Sci. 23 (2013) 427-456. PDF file ,
      doi:10.1007/s00332-012-9157-y

  • X. Chen and J.-G. Liu,
    • Global weak entropy solution to Doi-Saintillan-Shelley model for active and passive rod-like and ellipsoidal particle suspensions
    J Diff Eqs, 254 (2013) 2764-2802. PDF file ,
      doi:10.1016/j.jde.2013.01.005

  • S. Jin, J.-G. Liu and L. Wang
    • A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations
    Math. Comp. 82 (2013) 749--779. PDF file ,
      doi:10.1090/S0025-5718-2012-02643-3

    2012:

  • D. Chae and J.-G. Liu
    • Blow-up, zero alpha limit and the Liouville type theorem for the Euler-Poincare equations
    Comm. Math. Phy., 314 (2012) 671-687 PDF file ,
      doi:10.1007/s00220-012-1534-8

  • X. Chen and J.-G. Liu
    • Two nonlinear compactness theorems in L^p(0,T;B)
    Appl. Math. Lett., 25 (2012) 2252-2257. PDF file ,
      doi:10.1016/j.aml.2012.06.012

  • L. Chen, J.-G. Liu and J. Wang
    • Multi-dimensional degenerate Keller-Segel system with critical diffusion exponent 2n/(n+2)
    SIAM J. Math Anal, 44 (2012) 1077-1102 PDF file ,
      doi:10.1137/110839102

  • A. Frouvelle and J.-G. Liu
    • Dynamics in a kinetic model of oriented particles with phase transition
    SIAM J. Math Anal, 44 (2012) 791--826. PDF file ,
      doi:10.1137/110823912

  • J. Carrillo, L. Chen, J.-G. Liu and J. Wang
    • A note on the subcritical two dimensional Keller-Segel system
    Acta Appl. Math., 119 (2012) 43-55. PDF file ,
      doi:10.1007/s10440-011-9660-4

  • P. Degond and J.-G. Liu
    • Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation
    Math. Models Methods Appl. Sci. 22 (2012) 1114001-18 PDF file ,
      doi:10.1142/S021820251140001X

  • A. Chertock, J.-G. Liu, and T. Pendleton
    • Convergence of a particle method and global weak solutions of a family of evolutionary PDEs
    SIAM J. Numer. Anal., 50 (2012) 1-21. PDF file ,
      doi:10.1137/110831386

  • J. Haack, S. Jin and J.-G. Liu
    • An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations
    Commun. Comput. Phy. 12 (2012) 955--980. PDF file ,
      doi:10.4208/cicp.250910.131011a

  • A. Chertock, J.-G. Liu, and T. Pendleton
    • Convergence analysis of the particle method for the Camassa-Holm equation
    "Proceedings of the Thirteenth International Conference on Hyperbolic Problems: Theory, Numerics and Application", (Ta-Tsien Li and Song Jiang, eds), Series in Contemporary Applied Mathematics CAM vol 17, Higher Education Press, Beijing, (2012), 365-373. PDF file

    2011:

  • W. Zheng, H. Gao, J.-G.-Liu, Y. Zhang, Q. Ye and C. Swank
    • General solution to gradient-induced transverse and longitudinal relaxation of spins undergoing restricted diffusion
    Phys. Rev. A 84 (2011) 053411. PDF file ,
      doi:10.1103/PhysRevA.84.053411

  • M. Acheritogaray, P. Degond, A. Frouvelle, and J.-G. Liu
    • Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system
    Kinetic & Related Models 4 (2011) 901-918. PDF file ,
      doi:10.3934/krm.2011.4.901

  • Y.-L. Huang, J.-G. Liu and W.-C. Wang
    • An FFT based fast Poisson solver on spherical shells
    Commun. Comput. Phy. 9 (2011) 649-667 PDF file ,
      doi:10.4208/cicp.060509.080609s

  • J.-G. Liu and A. Lorz
    • A coupled chemotaxis-fluid model: Global existence
    Ann. I. H. Poincare, AN 28 (2011) 643-652 PDF file ,
      doi:10.1016/j.anihpc.2011.04.005

    2010:

  • J.-G. Liu, J. Liu and R. Pego,
    • Stable and accurate pressure approximation for unsteady incompressible viscous flow
    J. Comput. Phys. 229 (2010) 3428-3453 PDF file ,
      doi:10.1016/j.jcp.2010.01.010

  • J.-G. Liu and R. Pego,
    • Stable discretization of magnetohydrodynamics in bounded domains
    Commun. Math. Sci. 8 (2010), 234 - 251 PDF file ,
      doi:10.4310/CMS.2010.v8.n1.a12

  • J.-G. Liu and L. Mieussens,
    • Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit
    SIAM J. Numer. Anal. 48 (2010), 1474-1491 PDF file ,
      doi:10.1137/090772770

    2009:

  • S.-Y. Ha and J.-G. Liu
    • A simple proof of the Cucker-Smale flocking dynamics and mean-field limit
    Comm. Math. Sci. 7 (2009), 297 - 325 PDF file ,
      doi:10.4310/CMS.2009.v7.n2.a2

  • J.-G. Liu and W.-C. Wang
    • Characterization and regularity for axisymmetric solenoidal vector elds with application to Navier-Stokes equation
    SIAM J. Math. Anal. 41 (2009) 1825-1850. PDF file ,
      doi:10.1137/080739744

  • E. Tadmor, J.-G. Liu, and A.E. Tzavaras (editors)
    • Hyperbolic Problems: Theory, Numerics and Applications, volume I: Plenary & Invited Talks ; volume II: Contributed Talks.
    Proceedings of Symposia in Applied Mathematics, Volume 67,
    American Mathematical Society, 2009 ISBN-10: 0-8218-4728-7, ISBN-13: 978-0-8218-4728-2.

  • T. Hou, C. Liu and J.-G. Liu (editors)
    • Multi-scale Phenomena in Complex Fluids, Modeling, Analysis and Numerical Simulations ,
    World Scientific, 2009, ISBN 978-981-4273-25-1, 981-4273-25-2

  • J.-G. Liu, J. Liu and R. Pego,
    • Error estimates for finite-element Navier-Stokes solvers without standard inf-sup conditions
    Chin. Ann. Math. Ser. B 30 (2009) 743-768. PDF file ,
      doi:10.1007/s11401-009-0116-3

    2008:

  • J.-G. Liu and C. Wang,
    • A fourth order numerical method for the primitive equations formulated in mean vorticity
    Commun. Comput. Phys. 4 (2008), 26 - 55 PDF file
    https://www.global-sci.com/intro/article_detail/cicp/7780.html

  • P. Lin, J.-G. Liu and X. Lu,
    • Long time numerical solutyion of the Navier-Stokes equations based on a sequential regularization formulation
    SIAM J. Sci. Comput. 31 (2008), 398--419 PDF file ,
      doi:10.1137/060673722

  • P. Degond, J.-G. Liu and M-H Vignal,
    • Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit
    SIAM J. Num. Anal., 46 (2008), 1298--1322 PDF file ,
      doi:10.1137/070690584

  • X. Lu, P. Lin and J.-G. Liu,
    • Analysis of a sequential regularization method for the unsteady Navier-Stokes equations
    Math. Comp., 77 (2008) 1467--1494. PDF file ,
      doi:10.1090/S0025-5718-08-02087-5

  • C.-H. Hsia, J.-G. Liu and C. Wang,
    • Structural stability and bifurcation for 2D incompressible flows with symmetry
    Methods and Applications of Analysis, 15 (2008) 495--512. PDF file ,
      doi:10.4310/MAA.2008.v15.n4.a6

    2007:

  • J.-G. Liu, Jie Liu and R. Pego,
    • Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate
    Comm. Pure App. Math., 60 (2007) 1443--1487. PDF file ,
      doi:10.1002/cpa.20178

  • W. Bao and J.-G. Liu (editors)
    • Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization ,
    World Scientific, 2007, SBN-10: 9812708502, ISBN-13: 9789812708502.

  • S. Antman and J.-G. Liu
    • Basic themes and pretty problems of nonlinear solid mechanics
    Milan J. Math, 75 (2007) 135--176. PDF file ,
      doi:10.1007/s00032-007-0068-6

  • P. Degond, S. Jin and J.-G. Liu,
    • Mach-number uniform asymptotic-preserving Gauge schemes for compressible flows
    Bulletin of the Institute of Mathematics Academia Sinica (New Series) 2 (2007), no. 4, 851--892. PDF file
    https://web.math.sinica.edu.tw/bulletin/archives_articlecontent16.jsp?bid=MjAwNzQwMw==

  • J.-G. Liu, Jie Liu and R. Pego,
    • Estimates on the Stokes pressure by partitioning the energy of harmonic functions ,
    in "Kyoto Conference on the Navier-Stokes equations and their Applications",
    edited by Y. Giga, H. Kozono, H. Okamoto and Y. Shibta, RIMS Kokyuroku Bessatsu B1, Kyoto Univ. (2007) 251--270. PDF file

  • J. Moore, Z. Cheng, J. Hao, G. Guo, J.-G. Liu, C. Lin and L. Yu,
    • Effects of solid-state yeast treatment on the antioxidant properties and protein and fiber compositions of common hard wheat bran
    J Agric Food Chem, (2007), 55, 10173--10182. PDF file ,
      doi:10.1021/jf071590o

    2006:

  • P. Degond, J.-G. Liu and L. Mieussens,
    • Macroscopic fluid modes with localized kinetic upscaling effects
    Multiscale Model. Simul. 5 (2006) 695--1043 PDF file ,
      doi:10.1137/060651574

  • J.-G. Liu and W.C. Wang,
    • Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows
    SIAM J Numer. Anal. 44 (2006) 2456-2480. PDF file ,
      doi:10.1137/050639314

  • J.-G. Liu, Jie Liu and R. Pego,
    • On incompressible Navier-Stokes dynamics: a new approach for analysis and computation
    in "Proceedings of the Tenth International Conference on Hyperbolic Problems",
    edited by F. Asakura, etc, Yokohama Publishers, Inc. (2006) 29--44. PDF file

  • J.-G. Liu, R. Samelson and C. Wang,
    • Global weak solution of planetary geostrophic equations with inviscid geostrophic balance
    Appl. Anal., 85 (2006), 593 - 605 PDF file ,
      doi:10.1080/00036810500328299

  • J. Moore, J.-G. Liu, K. Zhou, S. Haley, and L. Yu,
    • Effects of genotype and environment on the antioxidant properties of hard winter wheat bran
    J Agric Food Chem, (2006), 54, 5313--5322. PDF file ,
      doi:10.1021/jf060381l

    2004:

  • H. Johnston and J.-G. Liu,
    • Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term
    J. Comput. Phys. 188 (2004) 221-259. PDF file ,
      doi:10.1016/j.jcp.2004.02.009

  • B. Li and J.-G. Liu,
    • Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling
    J. Nonlinear Sci., 14 (2004) 429-451. PDF file ,
      doi:10.1007/s00332-004-0634-9

  • M. Ghil, J.-G. Liu, C. Wang and S. Wang,
    • Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow
    Physica D, 197 (2004) 149--173. PDF file ,
      doi:10.1016/j.physd.2004.06.012

  • J.-G. Liu and W.C. Wang,
    • Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry
    J. Comput. Phys., 200 (2004) 8-33. PDF file ,
      doi:10.1016/j.jcp.2004.03.005

  • J.-G. Liu and C. Wang
    • High order finite difference method for unsteady incompressible flow on multi-connected domain in vorticity-stream function formulation
    Comput Fluids, 33 (2004) 223-255. PDF file ,
      doi:10.1016/S0045-7930(03)00037-9

  • C. Wang, J.-G. Liu and H. Johnston,
    • Analysis of a fourth order finite difference method for the incompressible Boussinesq equations
    Numer. Math., 97 (2004) 555--594. PDF file ,
      doi:10.1007/s00211-003-0508-3

  • J.-G. Liu, and W.-Q. Xu,
    • Far field boundary condition for convection diffusion equation at zero viscosity limit
    Quart. Appl. Math 62 (2004) 27-52. PDF file ,
      doi:10.1090/qam/2032571

  • H.-E. Lin, J.-G. Liu, and W.-Q. Xu,
    • Effects of small viscosity and far field boundary conditions for hyperbolic systems
    Commun. Pure Appl. Anal. 3 (2004) 267-290. PDF file ,
      doi:10.3934/cpaa.2004.3.267

    2003:

  • Weinan E and J.-G. Liu,
    • Gauge method for viscous incompressible flows
    Comm. Math. Sci., 1 (2003), 317--332. PDF file ,
      doi:10.4310/CMS.2003.v1.n2.a6

  • B. Li and J.-G. Liu,
    • Thin film epitaxy with or without slope selection
    European J. Applied Math., 14 , (2003) 713-743. PDF file ,
      doi:10.1017/S095679250300528X

  • I.-L. Chern, J.-G. Liu and W.-C. Wang,
    • Accurate Evaluation of Electrostatics for Macromolecules in Solution ,
    Methods and Applications of Analysis, 10 (2003) 309-328. PDF file ,
      doi:10.4310/MAA.2003.v10.n2.a9

  • C. Chainais-Hillairet, J.-G. Liu and Y.-J. Peng,
    • Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
    Math. Model. Numer. Anal., 37 (2003) 319-338. PDF file ,
      doi:10.1051/m2an:2003028

  • J.-G. Liu, C. Wang and H. Johnston,
    • A fourth order compact scheme for incompressible Boussinesq equations
    J. Sci. Comput. 18 (2003) 253-285. PDF file ,
      doi:10.1023/A:1021168924020

  • K. Duraisamy, J.D. Baeder and J.-G. Liu,
    • Concepts and application of time limiters to high resolution schemes
    J. Sci. Comput. 19 (2003) 139-162. PDF file ,
      doi:10.1023/A:1025395707090

  • C. Wang and J.-G. Liu,
    • Positivity property of second-order flux-splitting schemes for the compressible Euler equations
    Discrete Contin. Dyn. Syst. Ser. B 3 (2003) 201-228. PDF file ,
      doi:10.3934/dcdsb.2003.3.201

  • C. Wang and J.-G. Liu,
    • Fourth order convergence of a compact difference solver for incompressible flow
    Commun. Appl. Anal. 7 , (2003), 171-191.

    2002:

  • H. Johnston and J.-G. Liu,
    • Finite difference schemes for incompressible flow based on local pressure boundary condition
    J. Comput. Phys. 180 (2002), 120--154. PDF file ,
      doi:10.1006/jcph.2002.7079

  • Weinan E and J.-G. Liu,
    • Projection method III: spatial discretization on the staggered grid
    Math. Comp. 71 (2002), 27--47. PDF file ,
      doi:10.1090/S0025-5718-01-01313-8

  • C. Wang and J.-G. Liu,
    • Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation
    Numer. Math. 91 (2002), 543--576. PDF file ,
      doi:10.1007/s002110100311

    2001:

  • J.-G. Liu and Z. Xin,
    • Convergence of point vortex method for 2-D vortex sheet
    Math. Comp. 70 (2001) 565-606. PDF file ,
      doi:10.1090/S0025-5718-00-01271-0

  • J.-G. Liu and Weinan E
    • Simple finite element method in vorticity formulation for incompressible flow
    Math. Comp. 69 (2001) 1385-1407. PDF file ,
      doi:10.1090/S0025-5718-00-01239-4

  • J.-G. Liu and W.C. Wang,
    • An energy preserving MAC-Yee scheme for the incompressible MHD equation
    J. Comput. Phys. 174 (2001), 12--37. PDF file ,
      doi:10.1006/jcph.2001.6772

    2000:

  • Weinan E and J.-G. Liu,
    • Gauge finite element method for incompressible flows
    Int. J. Num. Meth. Fluids, 34 (2000) 701-710. PDF file ,
      doi:10.1002/1097-0363(20001230)34:8<701::AID-FLD76>3.0.CO;2-B

  • C. Wang and J.-G. Liu,
    • Convergence of gauge method for incompressible flow
    Math. Comp. 69 (2000), 1385-1407. PDF file ,
      doi:10.1090/s0025-5718-00-01248-5

  • J.-G. Liu and C.-W. Shu,
    • A high order discontinuous Galerkin method for incompressible flows
    J. Comput. Phys. 160 (2000) 577-596. PDF file ,
      doi:10.1006/jcph.2000.6475

  • J.-G. Liu and Z. Xin,
    • Convergence of a Galerkin method for 2-D discontinuous Euler flows
    Comm. Pure Appl. Math. 53 (2000) 786-798. PDF file ,
      doi:10.1002/(SICI)1097-0312(200006)53:6<786::AID-CPA3>3.0.CO;2-Y

    1999:

  • Z.J. Wang, S. Childress and J.-G. Liu,
    • Connection between corner vortices and shear layer instability in flow past an ellipse
    Phys. Fluids. 11 (1999) 2446-2448. PDF file ,
      doi:10.1063/1.870108

  • P. Lefloch and J.-G. Liu,
    • Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions
    Math. Comp. 68 (1999) 1025-1055. PDF file ,
      doi:10.1090/s0025-5718-99-01062-5

    1998:

  • H. Choi and J.-G. Liu,
    • The reconstruction of upwind fluxes for conservation laws, its behavior in dynamic and steady state calculations
    J. Comput. Phys. 144 (1998) 237--256. PDF file ,
      doi:10.1006/jcph.1998.5970

  • E. Xu and J.-G. Liu,
    • Pricing of mortgage-backed securities with option-adjusted spread
    Managerial Finance, 24 (1998) 94-109. PDF file ,
      doi:10.1108/03074359810765796

    1997:

  • Weinan E and J.-G. Liu,
    • Finite difference schemes for incompressible flows in the impulse-velocity formulation
    J. Comput. Phys. 130 (1997) 67-76. PDF file ,
      doi:10.1006/jcph.1996.5537

  • G.-Q. Chen and J.-G. Liu,
    • Convergence of difference schemes with high resolutions to conservation laws
    Math. Comp. 66 (1997) 1027--1053. PDF file ,
      doi:10.1090/s0025-5718-97-00859-4

  • Weinan E and J.-G. Liu,
    • Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on non-staggered grids
    J. Comput. Phys. 138 (1997) 57--82. PDF file ,
      doi:10.1006/jcph.1997.5815

    1996:

  • J.-G. Liu and Z. Xin,
    • Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation
    Arch. Rat. Mech. Anal. 135 (1996) 61--105. PDF file
    Received a Featured Review from Math. Rev. ,
      doi:10.1007/BF02198435

  • J.-G. Liu and Z. Xin,
    • Kinetic and viscous boundary layers for the Broadwell equations
    Transport Theory Statist. Phys. 25 (1996) 447--461. PDF file ,
      doi:10.1080/00411459608220713

  • C.D. Levermore and J.-G. Liu,
    • Large oscillations arising from a dispersive numerical scheme
    Physica D, 99 (1996) 191-216. PDF file ,
      doi:10.1016/S0167-2789(96)00157-1

  • Weinan E and J.-G. Liu,
    • Projection method II: Godunov-Ryabenki analysis
    SIAM J. Numer. Anal., 33 (1996) 1597--1621. PDF file ,
      doi:10.1137/s003614299426450x

  • Weinan E and J.-G. Liu,
    • Essential compact scheme for unsteady viscous incompressible flows,
    J. Comput. Phys. 126 (1996) 122--138. PDF file ,
      doi:10.1006/jcph.1996.0125

  • Weinan E and J.-G. Liu,
    • Vorticity boundary condition and related issues for finite difference schemes
    J. Comput. Phys. 124 (1996) 368--382. PDF file ,
      doi:10.1006/jcph.1996.0066

  • W. E and J.-G. Liu,
    • Finite difference schemes for incompressible flows in the vorticity formulations
    ESAIM: Proceedings, 1 (1996) 181--195.
    PDF file ,
      doi:10.1051/proc:1996009

  • S. Jin and J.-G. Liu,
    • The effects of numerical viscosities I: slowly moving shocks
    J. Comput. Phys. 126 (1996) 373-389. PDF file ,
      doi:10.1006/jcph.1996.0144

  • S. Jin and J.-G. Liu,
    • Oscillations induced by numerical viscosities,
    Mat. Contemp. 10 (1996) 169-180. PDF file

    1995:

  • J.-G. Liu and Z. Xin,
    • Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheets data
    Comm. Pure Appl. Math. 48 (1995), 611-628. PDF file ,
      doi:10.1002/cpa.3160480603

  • Weinan E and J.-G. Liu,
    • Projection method I: convergence and numerical boundary layers,
    SIAM J. Numer. Anal., 32 (1995) 1017-1057. PDF file ,
      doi:10.1137/0732047

    1994:

  • S. Jin and J.-G. Liu,
    • Relaxation and diffusion enhanced dispersive waves
    Proc. Roy. Soc. Lon. A 446 (1994) 555-563. PDF file ,
      doi:10.1098/rspa.1994.0120

  • P. Lefloch and J.-G. Liu,
    • Discrete entropy and monotonicity criteria for hyperbolic conservation laws
    C.R. Acad. Sci. Paris. 319 (1994), 881--886. PDF file

    1993:

  • J.-G. Liu and Z. Xin,
    • Nonlinear stability of discrete shocks for systems of conservation laws
    Arch. Rat. Mech. Anal. 125 (1993), 217--256. PDF file ,
      doi:10.1007/BF00383220

  • J.-G. Liu and Z. Xin,
    • L1-stability of stationary discrete shocks
    Math. Comp. 60 (1993), 233--244. PDF file ,
      doi:10.2307/2153163

  • B. Engquist and J.-G. Liu,
    • Numerical methods for oscillatory solutions to hyperbolic problems
    Comm. Pure Appl. Math. 46 (1993), 1327--1361. PDF file ,
      doi:10.1002/cpa.3160461003

  • G.-Q. Chen and J.-G. Liu,
    • Convergence of second-order schemes for isentropic gas dynamics
    Math. Comp. 61 (1993), 607--629. PDF file ,
      doi:10.1090/S0025-5718-1993-1185239-7