Publications -- Jian-Guo Liu


Preprints:

  • P. Degond, M. Engel, J.-G. Liu, and R.L. Pego,
  • A Markov jump process modelling animal group size statistics
    submitted. arXiv:1901.01169

  • Yu Gao, Yuan Gao and J.-G. Liu,
  • Large time behavior, bi-Hamiltonian structure and kinetic formulation for complex Burgers equation
    submitted. arXiv:1812.09699

  • J.-G. Liu, R.L. Pego, Y. Pu,
  • Well-posedness and derivative blow-up for a dispersionless regularized shallow water system
    submitted. arXiv:1810.06096

  • L. Li, J.-G Liu, Z. Liu, J. Lu,
  • A stochastic version of Stein variational gradient descent for efficient sampling
    submitted. arXiv:1902.03394

  • 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
    submitted. arXiv:1902.00635

  • L. Li, J.-G. Liu
  • A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows
    submitted. arXiv:1901.03159

  • S. Jin, L. Li, J.-G. Liu,
  • Random batch methods (RBM) for interacting particle systems
    submitted. arXiv:1812.10575

  • L. Li, J.-G. Liu, P. Yu
  • On mean field limit for Brownian particles with Coulomb interaction in 3D
    submitted. arXiv:1811.07797

  • L. Li, J.-G. Liu,
  • Large time behaviors of upwind schemes by jump processes
    submitted. arXiv:1807.08396

  • J.-G. Liu, R.L. Pego and D. Slepčev,
  • Least action principles for incompressible flows and geodesics between shapes
    submitted. arXiv:1604.03387

  • Hui Huang, Jian-Guo Liu, Peter Pickl
  • On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system
    submitted. arXiv:1804.07002

  • J.-G. Liu and J. Wang,
  • On the best constant for Gagliardo-Nirenberg interpolation inequalities
    submitted. arXiv:1712.10208

  • J.-G. Liu and X. Xu,
  • On a class of functional inequalities and their applications to forth-order nonlinear parabolic equations,
    submitted. arXiv:1612.03508

    2019:

  • 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. PDF file

  • 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, to appear PDF file

  • A. Liu, J.-G. Liu and Y. Lu,
  • On the rate of convergence of empirical measure in infinity-Wasserstein distance for unbounded density function
    Quarterly of Applied Mathematics, to appear PDF file

  • A Frouvelle, J.G. Liu,
  • Long-time dynamics for a simple aggregation equation on the sphere
    To appear in The Institut Henri Poincaré trimester "Stochastic Dynamics out of Equilibrium", edited by G. Giacomin, S Olla, E Saada, H Spohn, and G Stoltz, Springer (2019). arXiv:1810.06904

  • 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, to appear, arXiv:1809.10649

  • J.-G. Liu and R.M. Strain,
  • Global stability for solutions to the exponential PDE describing epitaxial growth
    Interfaces and Free Boundaries, to appear. arXiv:1805.02246

  • 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, accepted arXiv:1802.00655

  • 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, Optimisation and Calculus of Variations, accepted arXiv:1710.06995

  • J.-G. Liu, J. Lu, D. Margetis and J.L. Marzuola,
  • Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model
    Physica D, accepted PDF file

  • J.-G. Liu and R. Pego,
  • On local singularities in ideal potential flows with free surface,
    Chin. Ann. Math, to appear PDF file

  • J.-G. Liu, B. Niethammer, and R. Pego,
  • Self-similar spreading in a merging-splitting model of animal group size
    J. Stat Phys, to appear PDF file

  • K. Lafata, Z. Zhou, J.-G. Liu, F.F. Yin,
  • Data clustering based on Langevin annealing with a self-consistent potential.
    Quarterly of Applied Mathematics, to appear PDF file

  • 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

  • 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

  • Hui Huang, Jian-Guo Liu, and Jianfeng Lu
  • Learning interacting particle systems: diffusion parameter estimation for aggregation equations
    Mathematical Models and Methods in Applied Sciences, 29 (2019) 1-29 PDF file

  • 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
    Physics in Medicine and Biology. 64 (2019) 025007. PDF file

    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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • K. Chen, Q. Li, and J.-G. Liu,
  • Online learning in optical tomography: a stochastic approach
    Inverse Problems, 34 (2018) 075010. PDF file

  • 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

  • L. Li, J.-G. Liu, and L. Wang,
  • Cauchy problems for Keller-Segel type time-space fractional diffusion equation
    Journal of Differential Equations, 265 (2018) 1044-1096. PDF file

  • L. Li and J.-G. Liu,
  • p-Euler equations and p-Navier-Stokes equations,
    Journal of Differential Equations, 264 (2018) 4707-4748. PDF file

  • 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
    Calculus of Variations and PDE, (2018) 57:55. PDF file

  • J.-G. Liu and X. Xu,
  • Partial regularity for weak solutions to a PDE system with cubic nonlinearities,
    Journal of Differential Equations, 264 (2018) 5489-5526. PDF file

  • Y. Feng, L. Li, J.-G. Liu and X. Xu,
  • A note on one-dimensional time fractional ODEs,
    Applied Math Letter, 83 (2018) 87-94. PDF file

  • 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

  • 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

  • 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

    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

  • 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

  • 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

  • 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

  • P. Degond, M. Herty, J.-G. Liu,
  • Meanfield games and model predictive control
    Comm Math Science, 15 (2017) 1403--1422. PDF file

  • 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

  • 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

  • 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

  • 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

  • Y. Gao, J.-G. Liu, J. Lu,
  • Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces
    J. Nonlinear Science, 27 (2017), 873--926. PDF file

  • 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

  • P. Degond, J.-G. Liu, and R.L. Pego
  • Coagulation-fragmentation model for animal group-size statistics
    J. Nonlinear Science, 27 (2017) 379--424. PDF file

  • 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

  • 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

  • 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

  • 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

  • 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

    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

  • 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

  • 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

  • J. Chen, J.-G. Liu and Z. Zhou,
  • On a Schrodinger-Landau-Lifshitz system: Variational structure and numerical methods
    Multiscale Modeling and Simulation, 14 (2016) 1463-1487. PDF file

  • J.-G. Liu and R.L. Pego
  • On generating functions of Hausdorff moment sequences
    Trans. Amer. Math. Soc. 368 (2016) 8499-8518 PDF file

  • W. Cong and J.-G. Liu,
  • A degenerate p-Laplacian Keller-Segel model
    Kinet. Relat. Models, 9 (2016) 687--714. PDF file

  • H. Huang and J.-G. Liu,
  • Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos
    Kinet. Relat. Models, 9 (2016) 715--748. PDF file

  • 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

  • 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

  • H. Huang and J.-G. Liu,
  • A note on Monge-Ampere Keller-Segel equation
    Applied Math Letter, 61 (2016) 26-34 PDF file

  • 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

  • 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

  • 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

  • J.-G. Liu and J. Wang,
  • Refined hyper-contractivity and uniqueness for the Keller-Segel equations
    Applied Math Letter, 52 (2016) 212-219 PDF file

    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 Applied Math, 75 (2015) 2246-2267 PDF file

  • 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

  • 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

  • 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

  • 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

    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

  • 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

  • X. Chen, A. Jungel, J.-G. Liu
  • A note on Aubin-Lions-Dubinskii lemmas
    Acta Appl. Math., 133 (2014) 33-43 PDF file

  • 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

  • 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
    Commun. Math. Sci., 12 (2014) 1579-1601. PDF file

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

  • 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

  • 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,
    Internat. J. Numer. Methods Fluids, 75 (2014) 81-154. PDF file

  • 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

  • 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

  • S. Bian, J.-G. Liu, and C. Zou,
  • Ultra-contractivity for Keller-Segel model with diffusion exponent m>1-2/d
    Kinet. Relat. Models, 7 (2014) 9-28. PDF file

  • 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

    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

  • P. Degond, J.-G, Liu, S. Motsch, V. Panferov
  • Hydrodynamic models of self-organized dynamics: derivation and existence theory
    Methods Anal. Appl. 20 (2013) 89-114. PDF file

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

    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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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
    Kinet. Relat. 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

    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

  • 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

    2009:

  • S.-Y. Ha and J.-G. Liu
  • A simple proof of the Cucker-Smale flocking dynamics and mean-field limit
    Commun. Math. Sci. 7 (2009), 297 - 325 PDF file

  • 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

  • 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

    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

  • 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

  • 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

  • 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

  • C.-H. Hsia, J.-G. Liu and C. Wang,
  • Structural stability and bifurcation for 2D incompressible flows with symmetry
    Meth. Appl. Anal., 15 (2008) 495--512. PDF file

    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

  • 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

  • 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

  • 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

    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

  • 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

  • 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
    Applicable Analysis, 85 (2006), 593 - 605 PDF file

  • 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

    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

  • 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

  • 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

  • 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

  • J.-G. Liu and C. Wang
  • High order finite difference method for unsteady incompressible flow on multi-connected domain in vorticity-stream function formulation
    Computer and Fluids, 33 (2004) 223-255. PDF file

  • 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

  • J.-G. Liu, and W.-Q. Xu,
  • Far field boundary condition for convection diffusion equation at zero viscosity limit
    Q APPL MATH vol 62 (2004) 27-52. PDF file

  • H.-E. Lin, J.-G. Liu, and W.-Q. Xu,
  • Effects of small viscosity and far field boundary conditions for hyperbolic systems
    Communications on Pure and Applied Analysis, vol 3 (2004) 267-290. PDF file

    2003:

  • Weinan E and J.-G. Liu,
  • Gauge method for viscous incompressible flows
    Comm. Math. Sci., 1 (2003), 317--332. PDF file

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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • Weinan E and J.-G. Liu,
  • Projection method III: spatial discretization on the staggered grid
    Math. Comp. 71 (2002), 27--47. PDF file

  • 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

    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

  • J.-G. Liu and Weinan E
  • Simple finite element method in vorticity formulation for incompressible flow
    Math. Comp. 69 (2001) 1385-1407. PDF file

  • 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

    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

  • C. Wang and J.-G. Liu,
  • Convergence of gauge method for incompressible flow
    Math. Comp. 69 (2000), 1385-1407. PDF file

  • 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

  • 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

    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

  • 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

    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

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

    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

  • 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

  • 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

    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.

  • 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

  • C.D. Levermore and J.-G. Liu,
  • Large oscillations arising from a dispersive numerical scheme
    Physica D, 99 (1996) 191-216. PDF file

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

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

  • 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

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

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

  • 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

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

    1994:

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

  • 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

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

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

  • G.-Q. Chen and J.-G. Liu,
  • Convergence of second-order schemes for isentropic gas dynamics
    Math. Comp. 61 (1993), 607--629. PDF file