Publications of Jian-Guo Liu

Books

  1. Multi-scale phenomena in complex fluids, Modeling, Analysis and Numerical Simulations, edited by T. Hou, C. Liu and J.-G. Liu (2009), World Scientific, ISBN 978-981-4273-25-1
  2. Hyperbolic Problems: Theory, Numerics and Applications, volume I: Plenary & Invited Talks; volume II: Contributed Talks, Proceedings of Symposia in Applied Mathematics, edited by E. Tadmor, J.-G. Liu, and A.E. Tzavaras, vol. 67 (2009), American Mathematical Society, ISBN 978-0-8218-4728-2
  3. Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization, edited by W. Bao and J.-G. Liu (2007), World Scientific, ISBN 9789812708502

Papers Published

  1. Feng, Y; Li, L; Liu, JG; Xu, X, EXISTENCE OF WEAK SOLUTIONS TO p-NAVIER-STOKES EQUATIONS, Discrete and Continuous Dynamical Systems - Series B, vol. 29 no. 4 (April, 2024), pp. 1868-1890, American Institute of Mathematical Sciences (AIMS)
  2. Stevens, JB; Riley, BA; Je, J; Gao, Y; Wang, C; Mowery, YM; Brizel, DM; Yin, F-F; Liu, J-G; Lafata, KJ, Radiomics on spatial-temporal manifolds via Fokker-Planck dynamics., Med Phys (January, 2024)
  3. Gao, Y; Liu, J-G, A Selection Principle for Weak KAM Solutions via Freidlin–Wentzell Large Deviation Principle of Invariant Measures, SIAM Journal on Mathematical Analysis, vol. 55 no. 6 (December, 2023), pp. 6457-6495, Society for Industrial & Applied Mathematics (SIAM)
  4. Gao, Y; Liu, J-G, Large Deviation Principle and Thermodynamic Limit of Chemical Master Equation via Nonlinear Semigroup, Multiscale Modeling & Simulation, vol. 21 no. 4 (December, 2023), pp. 1534-1569, Society for Industrial & Applied Mathematics (SIAM)
  5. Qi, D; Liu, J-G, High-order moment closure models with random batch method for efficient computation of multiscale turbulent systems., Chaos (Woodbury, N.Y.), vol. 33 no. 10 (October, 2023), pp. 103133
  6. Wang, Y; Li, X; Konanur, M; Konkel, B; Seyferth, E; Brajer, N; Liu, J-G; Bashir, MR; Lafata, KJ, Towards optimal deep fusion of imaging and clinical data via a model-based description of fusion quality., Med Phys, vol. 50 no. 6 (June, 2023), pp. 3526-3537
  7. Dou, X; Liu, JG; Zhou, Z, A TUMOR GROWTH MODEL WITH AUTOPHAGY: THE REACTION-(CROSS-)DIFFUSION SYSTEM AND ITS FREE BOUNDARY LIMIT, Discrete and Continuous Dynamical Systems - Series B, vol. 28 no. 3 (March, 2023), pp. 1964-1992, American Institute of Mathematical Sciences (AIMS)
  8. Gao, Y; Li, T; Li, X; Liu, JG, TRANSITION PATH THEORY FOR LANGEVIN DYNAMICS ON MANIFOLDS: OPTIMAL CONTROL AND DATA-DRIVEN SOLVER, Multiscale Modeling and Simulation, vol. 21 no. 1 (March, 2023), pp. 1-33, Society for Industrial & Applied Mathematics (SIAM)
  9. Qi, D; Liu, J-G, A random batch method for efficient ensemble forecasts of multiscale turbulent systems., Chaos (Woodbury, N.Y.), vol. 33 no. 2 (February, 2023), pp. 023113
  10. Gao, Y; Liu, JG; Wu, N, Data-driven efficient solvers for Langevin dynamics on manifold in high dimensions, Applied and Computational Harmonic Analysis, vol. 62 (January, 2023), pp. 261-309
  11. Liu, JG; Tang, Y; Zhao, Y, ON THE EQUILIBRIUM OF THE POISSON-NERNST-PLANCK-BIKERMANN MODEL EQUIPPING WITH THE STERIC AND CORRELATION EFFECTS, Communications in Mathematical Sciences, vol. 21 no. 2 (January, 2023), pp. 485-515
  12. Gao, Y; Liu, JG, Random Walk Approximation for Irreversible Drift-Diffusion Process on Manifold: Ergodicity, Unconditional Stability and Convergence, Communications in Computational Physics, vol. 34 no. 1 (January, 2023), pp. 132-172
  13. Gao, Y; Liu, J-G; Li, W, Master equations for finite state mean field games with nonlinear activations, Discrete and Continuous Dynamical Systems - B (2023), American Institute of Mathematical Sciences (AIMS)
  14. Gao, Y; Liu, J-G, Stochastic Chemical Reaction Systems in Biology, SIAM REVIEW, vol. 65 no. 2 (2023), pp. 593-+
  15. Gao, Y; Liu, JG, Revisit of Macroscopic Dynamics for Some Non-equilibrium Chemical Reactions from a Hamiltonian Viewpoint, Journal of Statistical Physics, vol. 189 no. 2 (November, 2022), Springer Science and Business Media LLC
  16. Craig, K; Liu, JG; Lu, J; Marzuola, JL; Wang, L, A proximal-gradient algorithm for crystal surface evolution, Numerische Mathematik, vol. 152 no. 3 (November, 2022), pp. 631-662
  17. Li, L; Liu, JG; Tang, Y, Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations, Communications in Computational Physics, vol. 32 no. 1 (July, 2022), pp. 41-82, Global Science Press
  18. Degond, P; Frouvelle, A; Liu, JG, FROM KINETIC TO FLUID MODELS OF LIQUID CRYSTALS BY THE MOMENT METHOD, Kinetic and Related Models, vol. 15 no. 3 (June, 2022), pp. 417-465, American Institute of Mathematical Sciences (AIMS)
  19. Liu, JG; Wang, Z; Zhang, Y; Zhou, Z, RIGOROUS JUSTIFICATION OF THE FOKKER-PLANCK EQUATIONS OF NEURAL NETWORKS BASED ON AN ITERATION PERSPECTIVE, SIAM Journal on Mathematical Analysis, vol. 54 no. 1 (January, 2022), pp. 1270-1312, Society for Industrial & Applied Mathematics (SIAM)
  20. Liu, JG; Zhang, Z, EXISTENCE of GLOBAL WEAK SOLUTIONS of p-NAVIER-STOKES EQUATIONS, Discrete and Continuous Dynamical Systems - Series B, vol. 27 no. 1 (January, 2022), pp. 469-486, American Institute of Mathematical Sciences (AIMS)
  21. Gao, Y; Liu, JG, PROJECTION METHOD FOR DROPLET DYNAMICS ON GROOVE-TEXTURED SURFACE WITH MERGING AND SPLITTING, SIAM Journal on Scientific Computing, vol. 44 no. 2 (January, 2022), pp. B310-B338
  22. Li, L; Liu, JG; Liu, Z; Yang, Y; Zhou, Z, On Energy Stable Runge-Kutta Methods for the Water Wave Equation and its Simplified Non-Local Hyperbolic Model, Communications in Computational Physics, vol. 32 no. 1 (January, 2022), pp. 222-258, Global Science Press
  23. Gao, Y; Liu, JG, Surfactant-dependent contact line dynamics and droplet spreading on textured substrates: Derivations and computations, Physica D: Nonlinear Phenomena, vol. 428 (December, 2021)
  24. Liu, J-G; Wang, Z; Xie, Y; Zhang, Y; Zhou, Z, Investigating the integrate and fire model as the limit of a random discharge model: a stochastic analysis perspective, Mathematical Neuroscience and Applications, vol. Volume 1 (November, 2021), Centre pour la Communication Scientifique Directe (CCSD)
  25. Gao, Y; Liu, JG; Liu, Z, Existence and rigidity of the vectorial peierls-nabarro model for dislocations in high dimensions, Nonlinearity, vol. 34 no. 11 (November, 2021), pp. 7778-7828
  26. Lafata, KJ; Chang, Y; Wang, C; Mowery, YM; Vergalasova, I; Niedzwiecki, D; Yoo, DS; Liu, J-G; Brizel, DM; Yin, F-F, Intrinsic radiomic expression patterns after 20 Gy demonstrate early metabolic response of oropharyngeal cancers., Med Phys, vol. 48 no. 7 (July, 2021), pp. 3767-3777
  27. Hu, J; Liu, JG; Xie, Y; Zhou, Z, A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: Numerical analysis and exploration, Journal of Computational Physics, vol. 433 (May, 2021)
  28. Liu, JG; Wang, J; Zhao, Y; Zhou, Z, Field model for complex ionic fluids: Analytical properties and numerical investigation, Communications in Computational Physics, vol. 30 no. 3 (January, 2021), pp. 874-902
  29. Liu, JG; Xu, X, Existence and incompressible limit of a tissue growth model with autophagy, SIAM Journal on Mathematical Analysis, vol. 53 no. 5 (January, 2021), pp. 5215-5242
  30. Li, Q; Liu, JG; Shu, R, Sensitivity analysis of burgers' equation with shocks, SIAM-ASA Journal on Uncertainty Quantification, vol. 8 no. 4 (January, 2021), pp. 1493-1521, Society for Industrial & Applied Mathematics (SIAM)
  31. Gao, Y; Liu, JG, Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface, Interfaces and Free Boundaries, vol. 23 no. 1 (January, 2021), pp. 103-158
  32. Gao, Y; Katsevich, AE; Liu, JG; Lu, J; Marzuola, JL, ANALYSIS OF A FOURTH-ORDER EXPONENTIAL PDE ARISING FROM A CRYSTAL SURFACE JUMP PROCESS WITH METROPOLIS-TYPE TRANSITION RATES, Pure and Applied Analysis, vol. 3 no. 4 (January, 2021), pp. 595-612, Mathematical Sciences Publishers
  33. Liu, JG; Tang, M; Wang, L; Zhou, Z, Toward understanding the boundary propagation speeds in tumor growth models, SIAM Journal on Applied Mathematics, vol. 81 no. 3 (January, 2021), pp. 1052-1076
  34. Gao, Y; Jin, G; Liu, J-G, Inbetweening auto-animation via Fokker-Planck dynamics and thresholding, Inverse Problems & Imaging, vol. 15 no. 5 (2021), pp. 843-843, American Institute of Mathematical Sciences (AIMS)
  35. Huang, H; Liu, JG; Pickl, P, On the Mean-Field Limit for the Vlasov–Poisson–Fokker–Planck System, Journal of Statistical Physics, vol. 181 no. 5 (December, 2020), pp. 1915-1965
  36. Gao, Y; Liu, JG; Lu, J; Marzuola, JL, Analysis of a continuum theory for broken bond crystal surface models with evaporation and deposition effects, Nonlinearity, vol. 33 no. 8 (August, 2020), pp. 3816-3845
  37. Gao, Y; Liu, JG, Large Time Behavior, Bi-Hamiltonian Structure, and Kinetic Formulation for a Complex Burgers Equation, Quarterly of Applied Mathematics, vol. 79 no. 1 (May, 2020), pp. 120-123
  38. Jin, S; Li, L; Liu, JG, Convergence of the random batch method for interacting particles with disparate species and weights, SIAM Journal on Numerical Analysis, vol. 59 no. 2 (March, 2020), pp. 746-768
  39. Jin, S; Li, L; Liu, JG, Random Batch Methods (RBM) for interacting particle systems, Journal of Computational Physics, vol. 400 (January, 2020)
  40. Feng, Y; Gao, T; Li, L; Liu, JG; Lu, Y, Uniform-in-time weak error analysis for stochastic gradient descent algorithms via diffusion approximation, Communications in Mathematical Sciences, vol. 18 no. 1 (January, 2020), pp. 163-188
  41. Degond, P; Engel, M; Liu, JG; Pego, RL, A markov jump process modelling animal group size statistics, Communications in Mathematical Sciences, vol. 18 no. 1 (January, 2020), pp. 55-89
  42. Li, L; Li, Y; Liu, JG; Liu, Z; Lu, J, A stochastic version of stein variational gradient descent for efficient sampling, Communications in Applied Mathematics and Computational Science, vol. 15 no. 1 (January, 2020), pp. 37-63, Mathematical Sciences Publishers
  43. Li, L; Liu, JG, Large time behaviors of upwind schemes and B-schemes for fokker-planck equations on R by jump processes, Mathematics of Computation, vol. 89 no. 325 (January, 2020), pp. 2283-2320, American Mathematical Society (AMS)
  44. Gao, Y; Liu, JG; Luo, T; Xiang, Y, Revisit of the peierls-nabarro model for edge dislocations in Hilbert space, Discrete and Continuous Dynamical Systems - Series B, vol. 22 no. 11 (January, 2020)
  45. LIU, JG; WANG, J, GLOBAL EXISTENCE FOR NERNST-PLANCK-NAVIER-STOKES SYSTEM IN RN, Communications in Mathematical Sciences, vol. 18 no. 6 (January, 2020), pp. 1743-1754
  46. LIU, JIANGUO; XU, X, A CLASS OF FUNCTIONAL INEQUALITIES AND THEIR APPLICATIONS TO FOURTH-ORDER NONLINEAR PARABOLIC EQUATIONS, Communications in Mathematical Sciences, vol. 18 no. 7 (January, 2020), pp. 1911-1948, International Press of Boston
  47. Gao, Y; Liu, J-G, Long time behavior of dynamic solution to Peierls–Nabarro dislocation model, Methods and Applications of Analysis, vol. 27 no. 2 (2020), pp. 161-198, International Press of Boston
  48. Gao, Y; Liu, J-G, A note on parametric Bayesian inference via gradient flows, Annals of Mathematical Sciences and Applications, vol. 5 no. 2 (2020), pp. 261-282, International Press of Boston
  49. Gao, Y; Liu, J-G, LONG TIME BEHAVIOR OF DYNAMIC SOLUTION TO PEIERLS-NABARRO DISLOCATION MODEL, METHODS AND APPLICATIONS OF ANALYSIS, vol. 27 no. 2 (2020), pp. 161-197
  50. Li, L; Liu, JG; Yu, P, On the mean field limit for Brownian particles with Coulomb interaction in 3D, Journal of Mathematical Physics, vol. 60 no. 11 (November, 2019)
  51. Liu, JG; Pego, RL, On Local Singularities in Ideal Potential Flows with Free Surface, Chinese Annals of Mathematics. Series B, vol. 40 no. 6 (November, 2019), pp. 925-948
  52. Liu, JG; Pego, RL; Pu, Y, Well-posedness and derivative blow-up for a dispersionless regularized shallow water system, Nonlinearity, vol. 32 no. 11 (October, 2019), pp. 4346-4376
  53. Liu, JG; Pego, RL; Slepčev, D, Least action principles for incompressible flows and geodesics between shapes, Calculus of Variations and Partial Differential Equations, vol. 58 no. 5 (October, 2019)
  54. Lafata, KJ; Zhou, Z; Liu, J-G; Hong, J; Kelsey, CR; Yin, F-F, An Exploratory Radiomics Approach to Quantifying Pulmonary Function in CT Images., Sci Rep, vol. 9 no. 1 (August, 2019), pp. 11509
  55. Liu, JG; Tang, M; Wang, L; Zhou, Z, Analysis and computation of some tumor growth models with nutrient: From cell density models to free boundary dynamics, Discrete and Continuous Dynamical Systems - Series B, vol. 24 no. 7 (July, 2019), pp. 3011-3035
  56. Zhan, Q; Zhuang, M; Zhou, Z; Liu, JG; Liu, QH, Complete-Q Model for Poro-Viscoelastic Media in Subsurface Sensing: Large-Scale Simulation with an Adaptive DG Algorithm, IEEE Transactions on Geoscience and Remote Sensing, vol. 57 no. 7 (July, 2019), pp. 4591-4599, Institute of Electrical and Electronics Engineers (IEEE)
  57. Liu, JG; Niethammer, B; Pego, RL, Self-similar Spreading in a Merging-Splitting Model of Animal Group Size, Journal of Statistical Physics, vol. 175 no. 6 (June, 2019), pp. 1311-1330
  58. Liu, JG; Lu, J; Margetis, D; Marzuola, JL, Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model, Physica D: Nonlinear Phenomena, vol. 393 (June, 2019), pp. 54-67
  59. Gao, Y; Li, L; Liu, JG, Patched peakon weak solutions of the modified Camassa–Holm equation, Physica D: Nonlinear Phenomena, vol. 390 (March, 2019), pp. 15-35
  60. Lafata, KJ; Hong, JC; Geng, R; Ackerson, BG; Liu, J-G; Zhou, Z; Torok, J; Kelsey, CR; Yin, F-F, Association of pre-treatment radiomic features with lung cancer recurrence following stereotactic body radiation therapy., Phys Med Biol, vol. 64 no. 2 (January, 2019), pp. 025007
  61. Huang, H; Liu, JG; Lu, J, Learning interacting particle systems: Diffusion parameter estimation for aggregation equations, Mathematical Models and Methods in Applied Sciences, vol. 29 no. 1 (January, 2019), pp. 1-29
  62. Frouvelle, A; Liu, JG, Long-Time Dynamics for a Simple Aggregation Equation on the Sphere, Springer Proceedings in Mathematics and Statistics, vol. 282 (January, 2019), pp. 457-479, ISBN 9783030150952
  63. Gao, Y; Liu, JG; Lu, XY, Gradient flow approach to an exponential thin film equation: Global existence and latent singularity, ESAIM - Control, Optimisation and Calculus of Variations, vol. 25 (January, 2019), pp. 49-49, E D P SCIENCES
  64. De Hoop, MV; Liu, JG; Markowich, PA; Ussembayev, NS, Plane-wave analysis of a hyperbolic system of equations with relaxation in ℝd, Communications in Mathematical Sciences, vol. 17 no. 1 (January, 2019), pp. 61-79
  65. Liu, A; Liu, JG; Lu, Y, On the rate of convergence of empirical measure in ∞-Wasserstein distance for unbounded density function, Quarterly of Applied Mathematics, vol. 77 no. 4 (January, 2019), pp. 811-829
  66. Li, L; Liu, JG, A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows, SIAM Journal on Numerical Analysis, vol. 57 no. 5 (January, 2019), pp. 2095-2120
  67. Zhan, Q; Zhuang, M; Fang, Y; Liu, J-G; Liu, QH, Green's function for anisotropic dispersive poroelastic media based on the Radon transform and eigenvector diagonalization., Proceedings. Mathematical, physical, and engineering sciences, vol. 475 no. 2221 (January, 2019), pp. 20180610
  68. Liu, JG; Strain, RM, Global stability for solutions to the exponential PDE describing epitaxial growth, Interfaces and Free Boundaries, vol. 21 no. 1 (January, 2019), pp. 61-86
  69. Lafata, K; Zhou, Z; Liu, JG; Yin, FF, Data clustering based on Langevin annealing with a self-consistent potential, Quarterly of Applied Mathematics, vol. 77 no. 3 (January, 2019), pp. 591-613
  70. Hu, W; Li, CJ; Li, L; Liu, J-G, On the diffusion approximation of nonconvex stochastic gradient descent, Annals of Mathematical Sciences and Applications, vol. 4 no. 1 (2019), pp. 3-32, International Press of Boston
  71. Liu, J-G; Yang, R, PROPAGATION OF CHAOS FOR THE KELLER-SEGEL EQUATION WITH A LOGARITHMIC CUT-OFF, METHODS AND APPLICATIONS OF ANALYSIS, vol. 26 no. 4 (2019), pp. 319-348
  72. Gao, Y; Ji, H; Liu, JG; Witelski, TP, A vicinal surface model for epitaxial growth with logarithmic free energy, Discrete and Continuous Dynamical Systems - Series B, vol. 23 no. 10 (December, 2018), pp. 4433-4453, American Institute of Mathematical Sciences (AIMS)
  73. Feng, Y; Li, L; Liu, JG; Xu, X, Continuous and discrete one dimensional autonomous fractional odes, Discrete and Continuous Dynamical Systems - Series B, vol. 23 no. 8 (October, 2018), pp. 3109-3135, American Institute of Mathematical Sciences (AIMS)
  74. Feng, Y; Li, L; Liu, JG; Xu, X, A note on one-dimensional time fractional ODEs, Applied Mathematics Letters, vol. 83 (September, 2018), pp. 87-94, Elsevier BV
  75. Li, L; Liu, JG; Wang, L, Cauchy problems for Keller–Segel type time–space fractional diffusion equation, Journal of Differential Equations, vol. 265 no. 3 (August, 2018), pp. 1044-1096, Elsevier BV
  76. Gao, Y; Liu, JG, The modified camassa-holm equation in lagrangian coordinates, Discrete and Continuous Dynamical Systems - Series B, vol. 23 no. 6 (August, 2018), pp. 2545-2592, American Institute of Mathematical Sciences (AIMS)
  77. Liu, JG; Tang, M; Wang, L; Zhou, Z, An accurate front capturing scheme for tumor growth models with a free boundary limit, Journal of Computational Physics, vol. 364 (July, 2018), pp. 73-94, Elsevier BV
  78. Chen, K; Li, Q; Liu, JG, Online learning in optical tomography: A stochastic approach, Inverse Problems, vol. 34 no. 7 (May, 2018), pp. 075010-075010, IOP Publishing
  79. Liu, JG; Xu, X, Partial regularity of weak solutions to a PDE system with cubic nonlinearity, Journal of Differential Equations, vol. 264 no. 8 (April, 2018), pp. 5489-5526, ACADEMIC PRESS INC ELSEVIER SCIENCE
  80. Li, L; Liu, JG, p-Euler equations and p-Navier–Stokes equations, Journal of Differential Equations, vol. 264 no. 7 (April, 2018), pp. 4707-4748, Elsevier BV
  81. Gao, Y; Liu, JG; Lu, XY; Xu, X, Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface, Calculus of Variations and Partial Differential Equations, vol. 57 no. 2 (April, 2018), Springer Nature
  82. Feng, Y; Li, L; Liu, JG, Semigroups of stochastic gradient descent and online principal component analysis: Properties and diffusion approximations, Communications in Mathematical Sciences, vol. 16 no. 3 (January, 2018), pp. 777-789
  83. Li, L; Liu, JG, Some compactness criteria for weak solutions of time fractional pdes, SIAM Journal on Mathematical Analysis, vol. 50 no. 4 (January, 2018), pp. 3963-3995, Society for Industrial & Applied Mathematics (SIAM)
  84. Gao, Y; Li, L; Liu, JG, A dispersive regularization for the modified camassa–holm equation, SIAM Journal on Mathematical Analysis, vol. 50 no. 3 (January, 2018), pp. 2807-2838, Society for Industrial & Applied Mathematics (SIAM)
  85. Li, L; Liu, JG, A generalized definition of caputo derivatives and its application to fractional odes, SIAM Journal on Mathematical Analysis, vol. 50 no. 3 (January, 2018), pp. 2867-2900, Society for Industrial & Applied Mathematics (SIAM)
  86. Li, L; Liu, JG, A note on deconvolution with completely monotone sequences and discrete fractional calculus, Quarterly of Applied Mathematics, vol. 76 no. 1 (January, 2018), pp. 189-198, American Mathematical Society (AMS)
  87. Coquel, F; Jin, S; Liu, JG; Wang, L, Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and glimm front sampling for scalar conservation laws, Mathematics of Computation, vol. 87 no. 311 (January, 2018), pp. 1083-1126, American Mathematical Society (AMS)
  88. Liu, JG; Wang, L; Zhou, Z, Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations, Mathematics of Computation, vol. 87 no. 311 (January, 2018), pp. 1165-1189, American Mathematical Society (AMS)
  89. Jin, S; Liu, J-G; Ma, Z, 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, vol. 4 no. 1 (December, 2017), Springer Science and Business Media LLC
  90. Li, L; Liu, JG; Lu, J, Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem, Journal of Statistical Physics, vol. 169 no. 2 (October, 2017), pp. 316-339, Springer Nature America, Inc
  91. Liu, JG; Ma, Z; Zhou, Z, Explicit and Implicit TVD Schemes for Conservation Laws with Caputo Derivatives, Journal of Scientific Computing, vol. 72 no. 1 (July, 2017), pp. 291-313, Springer Nature
  92. Gao, Y; Ji, H; Liu, JG; Witelski, TP, Global existence of solutions to a tear film model with locally elevated evaporation rates, Physica D: Nonlinear Phenomena, vol. 350 (July, 2017), pp. 13-25, Elsevier BV
  93. Gao, Y; Liu, JG; Lu, J, Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces, Journal of Nonlinear Science, vol. 27 no. 3 (June, 2017), pp. 873-926, Springer Nature
  94. Liu, JG; Wang, J, Global existence for a thin film equation with subcritical mass, Discrete and Continuous Dynamical Systems - Series B, vol. 22 no. 4 (June, 2017), pp. 1461-1492, American Institute of Mathematical Sciences (AIMS)
  95. Degond, P; Liu, JG; Pego, RL, Coagulation–Fragmentation Model for Animal Group-Size Statistics, Journal of Nonlinear Science, vol. 27 no. 2 (April, 2017), pp. 379-424, Springer Nature
  96. Cong, W; Liu, JG, Uniform L boundedness for a degenerate parabolic-parabolic Keller-Segel model, Discrete and Continuous Dynamical Systems - Series B, vol. 22 no. 2 (March, 2017), pp. 307-338, American Institute of Mathematical Sciences (AIMS)
  97. Gao, Y; Liu, JG; Lu, J, Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime, SIAM Journal on Mathematical Analysis, vol. 49 no. 3 (January, 2017), pp. 1705-1731, Society for Industrial & Applied Mathematics (SIAM)
  98. Liu, JG; Wang, J, A generalized Sz. Nagy inequality in higher dimensions and the critical thin film equation, Nonlinearity, vol. 30 no. 1 (January, 2017), pp. 35-60, IOP Publishing
  99. Huang, H; Liu, JG, Discrete-in-time random particle blob method for the Keller-Segel equation and convergence analysis, Communications in Mathematical Sciences, vol. 15 no. 7 (January, 2017), pp. 1821-1842, International Press of Boston
  100. Degond, P; Herty, M; Liu, JG, Meanfield games and model predictive control, Communications in Mathematical Sciences, vol. 15 no. 5 (January, 2017), pp. 1403-1422, International Press of Boston
  101. Degond, P; Liu, JG; Merino-Aceituno, S; Tardiveau, T, Continuum dynamics of the intention field under weakly cohesive social interaction, Mathematical Models and Methods in Applied Sciences, vol. 27 no. 1 (January, 2017), pp. 159-182, World Scientific Pub Co Pte Lt
  102. Liu, JG; Yang, R, A random particle blob method for the keller-segel equation and convergence analysis, Mathematics of Computation, vol. 86 no. 304 (January, 2017), pp. 725-745, American Mathematical Society (AMS)
  103. Gao, Y; Liu, JG, Global convergence of a sticky particle method for the modified Camassa-Holm equation, SIAM Journal on Mathematical Analysis, vol. 49 no. 2 (January, 2017), pp. 1267-1294, Society for Industrial & Applied Mathematics (SIAM)
  104. Liu, JG; Xu, X, Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions, SIAM Journal on Mathematical Analysis, vol. 49 no. 3 (January, 2017), pp. 2220-2245, Society for Industrial & Applied Mathematics (SIAM)
  105. Huang, H; Liu, JG, Error estimate of a random particle blob method for the Keller-Segel equation, Mathematics of Computation, vol. 86 no. 308 (January, 2017), pp. 2719-2744, American Mathematical Society (AMS)
  106. Huang, H; Liu, JG, Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations, Discrete and Continuous Dynamical Systems - Series B, vol. 21 no. 10 (December, 2016), pp. 3463-3478, American Institute of Mathematical Sciences (AIMS)
  107. Liu, J-G; Yang, R, Propagation of chaos for large Brownian particle system with Coulomb interaction, Research in the Mathematical Sciences, vol. 3 no. 1 (December, 2016), Springer Science and Business Media LLC
  108. Huang, H; Liu, JG, A note on Monge-Ampère Keller-Segel equation, Applied Mathematics Letters, vol. 61 (November, 2016), pp. 26-34, Elsevier BV
  109. Liu, JG; Wang, J, A Note on L∞-Bound and Uniqueness to a Degenerate Keller-Segel Model, Acta Applicandae Mathematicae, vol. 142 no. 1 (April, 2016), pp. 173-188, Springer Nature, ISSN 0167-8019
  110. Herschlag, G; Liu, JG; Layton, AT, Fluid extraction across pumping and permeable walls in the viscous limit, Physics of Fluids, vol. 28 no. 4 (April, 2016), pp. 041902-041902, AIP Publishing, ISSN 1070-6631
  111. Liu, J-G; Wang, J, Refined hyper-contractivity and uniqueness for the Keller–Segel equations, Applied Mathematics Letters, vol. 52 (February, 2016), pp. 212-219, Elsevier BV
  112. Chen, J; Liu, JG; Zhou, Z, On a Schrödinger-Landau-Lifshitz system: Variational structure and numerical methods, Multiscale Modeling and Simulation, vol. 14 no. 4 (January, 2016), pp. 1463-1487, Society for Industrial & Applied Mathematics (SIAM)
  113. Huang, H; Liu, JG, Well-posedness for the keller-segel equation with fractional laplacian and the theory of propagation of chaos, Kinetic and Related Models, vol. 9 no. 4 (January, 2016), pp. 715-748
  114. Cong, W; Liu, JG, A degenerate p-laplacian keller-segel model, Kinetic and Related Models, vol. 9 no. 4 (January, 2016), pp. 687-714, American Institute of Mathematical Sciences (AIMS)
  115. Liu, JG; Xu, X, Existence theorems for a multidimensional crystal surface model, SIAM Journal on Mathematical Analysis, vol. 48 no. 6 (January, 2016), pp. 3667-3687, Society for Industrial & Applied Mathematics (SIAM)
  116. Liu, JG; Pego, RL, On generating functions of hausdorff moment sequences, Transactions of the American Mathematical Society, vol. 368 no. 12 (January, 2016), pp. 8499-8518, American Mathematical Society (AMS)
  117. Liu, JG; Zhang, Y, Convergence of diffusion-drift many particle systems in probability under a sobolev norm, Proceedings of Particle Systems and Partial Differential Equations - III, Springer Proceedings in Mathematics and Statistics, vol. 162 (January, 2016), pp. 195-223, Springer International Publishing, ISBN 9783319321424
  118. Duan, Y; Liu, J-G, Error estimate of the particle method for the $b$-equation, Methods and Applications of Analysis, vol. 23 no. 2 (2016), pp. 119-154, International Press of Boston
  119. Liu, J-G; Zhang, Y, Convergence of stochastic interacting particle systems in probability under a Sobolev norm, Annals of Mathematical Sciences and Applications, vol. 1 no. 2 (2016), pp. 251-299, International Press of Boston
  120. Degond, P; Frouvelle, A; Liu, JG, Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics, Archive for Rational Mechanics and Analysis, vol. 216 no. 1 (April, 2015), pp. 63-115
  121. Xue, Y; Wang, C; Liu, JG, Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis, Journal of Scientific Computing, vol. 65 no. 3 (March, 2015), pp. 1189-1216, Springer Nature, ISSN 0885-7474
  122. Lu, J; Liu, JG; Margetis, D, Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 91 no. 3 (March, 2015), pp. 032403, ISSN 1539-3755
  123. Chertock, A; Liu, JG; Pendleton, T, Elastic collisions among peakon solutions for the Camassa-Holm equation, Applied Numerical Mathematics, vol. 93 (January, 2015), pp. 30-46, Elsevier BV, ISSN 0168-9274
  124. Herschlag, G; Liu, JG; Layton, AT, An exact solution for stokes flow in a channel with arbitrarily large wall permeability, SIAM Journal on Applied Mathematics, vol. 75 no. 5 (January, 2015), pp. 2246-2267, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1399
  125. Degond, P; Frouvelle, A; Liu, J-G; Motsch, S; Navoret, L, Macroscopic models of collective motion and self-organization, Séminaire Laurent Schwartz — EDP et applications, vol. 2012 - 2013 (November, 2014), pp. 1-27, Cellule MathDoc/CEDRAM
  126. Degond, P; Liu, J-G; Ringhofer, C, Evolution of wealth in a non-conservative economy driven by local Nash equilibria., Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, vol. 372 no. 2028 (November, 2014), pp. 20130394, The Royal Society, ISSN 1364-503X
  127. Coquel, F; Jin, S; Liu, JG; Wang, L, Well-Posedness and Singular Limit of a Semilinear Hyperbolic Relaxation System with a Two-Scale Discontinuous Relaxation Rate, Archive for Rational Mechanics and Analysis, vol. 214 no. 3 (October, 2014), pp. 1051-1084, ISSN 0003-9527
  128. Johnston, H; Wang, C; Liu, JG, A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier–Stokes Equations, Journal of Scientific Computing, vol. 60 no. 3 (September, 2014), pp. 612-626, Springer Nature, ISSN 0885-7474
  129. Duan, Y; Liu, JG, Convergence analysis of the vortex blob method for the b-equation, Discrete and Continuous Dynamical Systems- Series A, vol. 34 no. 5 (May, 2014), pp. 1995-2011, American Institute of Mathematical Sciences (AIMS), ISSN 1078-0947
  130. Bian, S; Liu, JG; Zou, C, Ultra-contractivity for keller-segel model with diffusion exponent m > 1-2/d, Kinetic and Related Models, vol. 7 no. 1 (March, 2014), pp. 9-28, American Institute of Mathematical Sciences (AIMS), ISSN 1937-5093
  131. Degond, P; Herty, M; Liu, JG, Flow on sweeping networks, Multiscale Modeling and Simulation, vol. 12 no. 2 (January, 2014), pp. 538-565, Society for Industrial & Applied Mathematics (SIAM), ISSN 1540-3459
  132. Chen, X; Li, X; Liu, JG, Existence and uniqueness of global weak solution to a kinetic model for the sedimentation of rod-like particles, Communications in Mathematical Sciences, vol. 12 no. 8 (January, 2014), pp. 1579-1601, International Press of Boston, ISSN 1539-6746
  133. Degond, P; Frouvelle, A; Liu, J-G, A NOTE ON PHASE TRANSITIONS FOR THE SMOLUCHOWSKI EQUATION WITH DIPOLAR POTENTIAL, in Proceedings of the Fourteenth International Conference on Hyperbolic Problems: Theory, Numerics and Application, edited by Ancona, F; Bressan, A; Marcati, P; Marson, A, HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, vol. 8 (January, 2014), pp. 179-192, AMER INST MATHEMATICAL SCIENCES-AIMS
  134. Chae, D; Degond, P; Liu, JG, Well-posedness for hall-magnetohydrodynamics, Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, vol. 31 no. 3 (January, 2014), pp. 555-565
  135. Goudon, T; Jin, S; Liu, J-G; Yan, B, Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density, International Journal for Numerical Methods in Fluids, vol. 75 no. 2 (2014), pp. 81-102, WILEY, ISSN 0271-2091
  136. Bian, S; Liu, JG, Dynamic and Steady States for Multi-Dimensional Keller-Segel Model with Diffusion Exponent m > 0, Communications in Mathematical Physics, vol. 323 no. 3 (November, 2013), pp. 1017-1070, Springer Nature, ISSN 0010-3616
  137. Chen, X; Liu, JG, Analysis of polymeric flow models and related compactness theorems in weighted spaces, SIAM Journal on Mathematical Analysis, vol. 45 no. 3 (October, 2013), pp. 1179-1215, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  138. Goudon, T; Jin, S; Liu, JG; Yan, B, Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows, Journal of Computational Physics, vol. 246 (August, 2013), pp. 145-164, Elsevier BV, ISSN 0021-9991
  139. Chen, X; Liu, JG, Global weak entropy solution to Doi-Saintillan-Shelley model for active and passive rod-like and ellipsoidal particle suspensions, Journal of Differential Equations, vol. 254 no. 7 (April, 2013), pp. 2764-2802, Elsevier BV, ISSN 0022-0396
  140. Huang, YL; Liu, JG; Wang, WC, A generalized mac scheme on curvilinear domains, SIAM Journal on Scientific Computing, vol. 35 no. 5 (January, 2013), pp. B953-B986, Society for Industrial & Applied Mathematics (SIAM), ISSN 1064-8275
  141. Degond, P; Liu, J-G; Ringhofer, C, Evolution of the Distribution of Wealth in an Economic Environment Driven by Local Nash Equilibria, Journal of Statistical Physics, vol. 154 no. 3 (2013), pp. 1-30, Springer Nature, ISSN 0022-4715
  142. Chen, X; Jüngel, A; Liu, J-G, A Note on Aubin-Lions-Dubinskiǐ Lemmas, Acta Applicandae Mathematicae, vol. 133 no. 1 (2013), pp. 1-11, ISSN 0167-8019
  143. Degond, P; Liu, J-G; Ringhofer, C, Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria, Journal of Nonlinear Science, vol. 24 no. 1 (2013), pp. 1-23, ISSN 0938-8974
  144. Chae, D; Degond, P; Liu, J-G, Well-posedness for Hall-magnetohydrodynamics, Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis, vol. 31 no. 3 (2013), pp. 555-565, Elsevier BV, ISSN 0294-1449
  145. Jin, S; Liu, JG; Wang, L, A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations, Math. Comp., vol. 82 no. 282 (2013), pp. 749-779, American Mathematical Society (AMS)
  146. Degond, P; Liu, J-G; Motsch, S; Panferov, V, Hydrodynamic models of self-organized dynamics: Derivation and existence theory, Methods and Applications of Analysis, vol. 20 no. 2 (2013), pp. 89-114, International Press of Boston
  147. A. Chertock, J.-G. Liu, and T. Pendleton, Convergence analysis of the particle method for the Camassa-Holm equation, in Proceedings of the 13th International Conference on ``Hyperbolic Problems: Theory, Numerics and Applications" (2012), pp. 365-373, Higher Education Press, Beijing
  148. Chae, D; Liu, JG, Blow-up, zero alpha limit and the Liouville type theorem for the Euler-Poincare equations, Comm. Math. Phy.,, vol. 314 no. 3 (2012), pp. 671-687, Springer Nature, ISSN 0010-3616
  149. Chen, X; Liu, JG, Two Nonlinear Compactness Theorems in L^p(0,T;B), Appl. Math. Lett., vol. 25 no. 12 (2012), pp. 2252-2257, Elsevier BV, ISSN 0893-9659
  150. Chen, L; Liu, JG; Wang, J, Multi-dimensional degenerate Keller-Segel system with critical diffusion exponent 2n/(n+2), SIAM J. Math Anal, vol. 44 no. 2 (2012), pp. 1077-1102, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  151. Frouvelle, A; Liu, JG, Dynamics in a kinetic model of oriented particles with phase transition, SIAM J. Math Anal, vol. 44 no. 2 (2012), pp. 791-826, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  152. Carrillo, J; Chen, L; Liu, JG; Wang, J, A note on the subcritical two dimensional Keller-Segel system, Acta Applicanda Mathematicae, vol. 119 no. 1 (2012), pp. 43-55, Springer Nature, ISSN 0167-8019
  153. Degond, P; Liu, JG, Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation, Math. Models Methods Appl. Sci., vol. 22 no. SUPPL.1 (2012), pp. 1114001-1114018, World Scientific Pub Co Pte Lt, ISSN 0218-2025
  154. Chertock, A; Liu, JG; Pendleton, T, Convergence of a particle method and global weak solutions of a family of evolutionary PDEs, SIAM J. Numer. Anal., vol. 50 no. 1 (2012), pp. 1-21, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  155. Haack, J; Jin, S; Liu, JG, An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations, Commun. Comput. Phy., vol. 12 no. 4 (2012), pp. 955-980, Global Science Press, ISSN 1815-2406
  156. Degond, P; Frouvell, A; Liu, JG, Macroscopic limits and phase transition in a system of self-propelled particles, J Nonlinear Sci., vol. 23 no. 3 (2012), pp. 427-456, Springer Nature, ISSN 0938-8974
  157. Zheng, W; Gao, H; Liu, JG; Zhang, Y; Ye, Q; Swank, C, General solution to gradient-induced transverse and longitudinal relaxation of spins undergoing restricted diffusion, Physical Review A - Atomic, Molecular, and Optical Physics, vol. 84 no. 5 (November, 2011), pp. 053411-8, American Physical Society (APS), ISSN 1050-2947
  158. Liu, JG; Lorz, A, A coupled chemotaxis-fluid model: Global existence, Ann. I. H. Poincare, AN, vol. 28 no. 5 (2011), pp. 643-652, Elsevier BV, ISSN 0294-1449
  159. Acheritogaray, M; Degond, P; Frouvelle, A; Liu, JG, Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system, Kinetic and Related Models, vol. 4 no. 4 (2011), pp. 901-918, American Institute of Mathematical Sciences (AIMS), ISSN 1937-5093
  160. Huang, YL; Liu, JG; Wang, WC, An FFT based fast Poisson solver on spherical shells, Commun. Comput. Phy., vol. 9 no. 3 (2011), pp. 649-667, Global Science Press, ISSN 1815-2406
  161. Liu, JG; Liu, J; Pego, RL, Stable and accurate pressure approximation for unsteady incompressible viscous flow, Journal of Computational Physics, vol. 229 no. 9 (January, 2010), pp. 3428-3453, Elsevier BV, ISSN 0021-9991
  162. Liu, JG; Pego, RL, Stable discretization of magnetohydrodynamics in bounded domains, Communications in Mathematical Sciences, vol. 8 no. 1 (January, 2010), pp. 235-251, International Press of Boston, ISSN 1539-6746
  163. Liu, JG; Mieussens, L, Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit, SIAM J. Numer. Anal., vol. 48 no. 4 (2010), pp. 1474-1491, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  164. Liu, JG; Pego, R, Stable discretization of magnetohydrodynamics in bounded domains, Commun. Math. Sci., vol. 8 no. 1 (2010), pp. 234-251, INT PRESS BOSTON, INC, ISSN 1539-6746
  165. Liu, JG; Liu, J; Pego, RL, Error estimates for finite-element Navier-Stokes solvers without standard Inf-Sup conditions, Chinese Annals of Mathematics. Series B, vol. 30 no. 6 (December, 2009), pp. 743-768, Springer Nature, ISSN 0252-9599
  166. Liu, JG; Wang, WC, Characterization and regularity for axisymmetric solenoidal vector elds with application to Navier-Stokes equation, SIAM J. Math. Anal., vol. 41 no. 5 (2009), pp. 1825-1850, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  167. Ha, SY; Liu, JG, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Commun. Math. Sci., vol. 7 no. 2 (2009), pp. 297-325, International Press of Boston, ISSN 1539-6746
  168. Degond, P; Liu, JG; Vignal, MH, Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit, SIAM Journal on Numerical Analysis, vol. 46 no. 3 (November, 2008), pp. 1298-1322, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  169. Lu, X; Lin, P; Liu, JG, Analysis of a sequential regularization method for the unsteady Navier-Stokes equations, Mathematics of Computation, vol. 77 no. 263 (July, 2008), pp. 1467-1494, American Mathematical Society (AMS), ISSN 0025-5718
  170. Lin, P; Liu, JG; Lu, X, Long time numerical solution of the Navier-Stokes equations based on a sequential regularization formulation, SIAM Journal on Scientific Computing, vol. 31 no. 1 (January, 2008), pp. 398-419, Society for Industrial & Applied Mathematics (SIAM), ISSN 1064-8275
  171. Liu, JG; Wang, C, A fourth order numerical method for the primtive equations formulated in mean vorticity, Communications in Computational Physics, vol. 4 no. 1 (January, 2008), pp. 26-55, ISSN 1815-2406
  172. Hsia, CH; Liu, JG; Wang, C, Structural stability and bifurcation for 2D incompressible ows with symmetry, Meth. Appl. Anal., vol. 15 (2008), pp. 495-512
  173. Antman, SS; Liu, JG, Basic themes and pretty problems of nonlinear solid mechanics, Milan Journal of Mathematics, vol. 75 no. 1 (December, 2007), pp. 135-176, Springer Nature, ISSN 1424-9286
  174. Moore, J; Cheng, Z; Hao, J; Guo, G; Liu, J-G; Lin, C; Yu, LL, Effects of solid-state yeast treatment on the antioxidant properties and protein and fiber compositions of common hard wheat bran., Journal of agricultural and food chemistry, vol. 55 no. 25 (December, 2007), pp. 10173-10182, ISSN 0021-8561 (published on Web 10/30/2007.)
  175. Liu, JG; Liu, J; Pego, RL, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Communications on Pure and Applied Mathematics, vol. 60 no. 10 (October, 2007), pp. 1443-1487, WILEY, ISSN 0010-3640
  176. 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 (2007), pp. 251--270, Kyoto Univ.
  177. Liu, JG; Liu, J; Pego, R, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate via a commutator estimate, Comm. Pure Appl. Math., vol. 60 (2007), pp. 1443-1487
  178. Degond, P; Jin, S; Liu, JG, Mach-number uniform asymptotic- preserving Gauge schemes for compressible flows, Bulletin of the Institute of Mathematics Academia Sinica (New Series), vol. 2 (2007), pp. 851-892
  179. Liu, JG; Wang, WC, Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows, SIAM Journal on Numerical Analysis, vol. 44 no. 6 (December, 2006), pp. 2456-2480, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  180. Degond, P; Liu, JG; Mieussens, L, Macroscopic fluid models with localized kinetic upscaling effects, Multiscale Modeling and Simulation, vol. 5 no. 3 (September, 2006), pp. 940-979, Society for Industrial & Applied Mathematics (SIAM), ISSN 1540-3459
  181. Moore, J; Liu, J-G; Zhou, K; Yu, LL, Effects of genotype and environment on the antioxidant properties of hard winter wheat bran., Journal of agricultural and food chemistry, vol. 54 no. 15 (July, 2006), pp. 5313-5322, ISSN 0021-8561
  182. 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 (2006), pp. 29--44, Yokohama Publishers, Inc.
  183. Liu, JG; Samelson, R; Wang, C, Global weak solution of planetary geostrophic equations with inviscid geostrophic balance, Applicable Analysis, vol. 85 no. 6-7 (2006), pp. 593-605
  184. Liu, JG; Wang, WC, Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry, Journal of Computational Physics, vol. 200 no. 1 (October, 2004), pp. 8-33, Elsevier BV
  185. Ghil, M; Liu, JG; Wang, C; Wang, S, Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow, Physica D: Nonlinear Phenomena, vol. 197 no. 1-2 (October, 2004), pp. 149-173, Elsevier BV, ISSN 0167-2789
  186. Li, B; Liu, JG, Epitaxial growth without slope selection: Energetics, coarsening, and dynamic scaling, Journal of Nonlinear Science, vol. 14 no. 5 (October, 2004), pp. 429-451, Springer Nature, ISSN 0938-8974
  187. Johnston, H; Liu, JG, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, Journal of Computational Physics, vol. 199 no. 1 (September, 2004), pp. 221-259, Elsevier BV
  188. Wang, C; Liu, JG; Johnston, H, Analysis of a fourth order finite difference method for the incompressible Boussinesq equations, Numerische Mathematik, vol. 97 no. 3 (May, 2004), pp. 555-594, Springer Nature
  189. Lin, HE; Liu, JG; Xu, WQ, Effects of small viscosity and far field boundary conditions for hyperbolic systems, Communications on Pure and Applied Analysis, vol. 3 no. 2 (January, 2004), pp. 267-290, American Institute of Mathematical Sciences (AIMS), ISSN 1534-0392
  190. Liu, JG; Xu, WQ, Far field boundary condition for convection diffusion equation at zero viscosity limit, Quarterly of Applied Mathematics, vol. 62 no. 1 (January, 2004), pp. 27-52, American Mathematical Society (AMS)
  191. Liu, JG; Wang, C, High order finite difference methods for unsteady incompressible flows in multi-connected domains, Computers and Fluids, vol. 33 no. 2 (January, 2004), pp. 223-255, Elsevier BV
  192. Li, B; Liu, JG, Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling, J. Nonlinear Sci., vol. 14 no. 5 (2004), pp. 429-451, ISSN 0938-8974
  193. Liu, JG; Wang, C, High order finite difference method for unsteady incompressible flow on multi-connected domain in vorticity-stream function formulation, Computer and Fluids, vol. 33 no. 2 (2004), pp. 223-255
  194. Duraisamy, K; Baeder, JD; Liu, JG, Concepts and Application of Time-Limiters to High Resolution Schemes, Journal of Scientific Computing, vol. 19 no. 1-3 (December, 2003), pp. 139-162, ISSN 0885-7474
  195. Li, B; Liu, JG, Thin film epitaxy with or without slope selection, European Journal of Applied Mathematics, vol. 14 no. 6 (December, 2003), pp. 713-743, Cambridge University Press (CUP)
  196. Liu, JG; Wang, C; Johnston, H, A Fourth Order Scheme for Incompressible Boussinesq Equations, Journal of Scientific Computing, vol. 18 no. 2 (April, 2003), pp. 253-285, ISSN 0885-7474
  197. Wang, C; Liu, JG, Positivity property of second-order flux-splitting schemes for the compressible Euler equations, Discrete and Continuous Dynamical Systems - Series B, vol. 3 no. 2 (January, 2003), pp. 201-228, American Institute of Mathematical Sciences (AIMS)
  198. Chainais-Hillairet, C; Liu, JG; Peng, YJ, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis, Mathematical Modelling and Numerical Analysis, vol. 37 no. 2 (January, 2003), pp. 319-338, E D P SCIENCES
  199. Weinan, E; Liu, JG, ADDENDUM TO “GAUGE METHOD FOR VISCOUS INCOMPRESSIBLE FLOWS”*, Communications in Mathematical Sciences, vol. 1 no. 4 (January, 2003), pp. 837-837
  200. Wang, C; Liu, JG, Fourth order convergence of a compact difference solver for incompressible flow, Commun. Appl. Anal., vol. 7 (2003), pp. 171-191
  201. Weinan, E; Liu, JG, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317-332
  202. Chern, IL; Liu, JG; Wang, WC, Accurate evaluation of electrostatics for macromolecules in solution, Methods and Applications of Analysis, vol. 10 (2003), pp. 309-328
  203. Johnston, H; Liu, JG, Finite difference schemes for incompressible flow based on local pressure boundary conditions, Journal of Computational Physics, vol. 180 no. 1 (July, 2002), pp. 120-154, Elsevier BV, ISSN 0021-9991
  204. Wang, C; Liu, JG, Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation, Numerische Mathematik, vol. 91 no. 3 (May, 2002), pp. 543-576
  205. Weinan, E; Liu, JG, Projection method III: Spatial discretization on the staggered grid, Mathematics of Computation, vol. 71 no. 237 (January, 2002), pp. 27-47, American Mathematical Society (AMS)
  206. Liu, JG; Wang, WC, An energy-preserving MAC-Yee scheme for the incompressible MHD equation, Journal of Computational Physics, vol. 174 no. 1 (November, 2001), pp. 12-37, Elsevier BV, ISSN 0021-9991
  207. Liu, JG; Xin, Z, Convergence of the point vortex method for 2-D vortex sheet, Mathematics of Computation, vol. 70 no. 234 (April, 2001), pp. 595-606, American Mathematical Society (AMS)
  208. Liu, JG; Weinan, E, Simple finite element method in vorticity formulation for incompressible flows, Mathematics of Computation, vol. 70 no. 234 (April, 2001), pp. 579-593, American Mathematical Society (AMS)
  209. Liu, JG; Weinan, E, Simple finite element method in vorticity formulation for incompressible flow, Math. Comp., vol. 69 (2001), pp. 1385-1407
  210. Liu, JG; Xin, Z, Convergence of point vortex method for 2-D vortex sheet, Math. Comp., vol. 70 no. 234 (2001), pp. 565-606
  211. Weinan, E; Liu, JG, Gauge finite element method for incompressible flows, International Journal for Numerical Methods in Fluids, vol. 34 no. 8 (December, 2000), pp. 701-710, WILEY, ISSN 0271-2091
  212. Liu, JG; Shu, CW, A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows, Journal of Computational Physics, vol. 160 no. 2 (May, 2000), pp. 577-596, Elsevier BV
  213. Liu, JG; Xin, Z, Convergence of a Galerkin method for 2-D discontinuous Euler flows, Communications on Pure and Applied Mathematics, vol. 53 no. 6 (January, 2000), pp. 786-798, Wiley
  214. Wang, C; Liu, JG, Convergence of gauge method for incompressible flow, Mathematics of Computation, vol. 69 no. 232 (January, 2000), pp. 1385-1407
  215. Lefloch, PG; Liu, JG, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions, Mathematics of Computation, vol. 68 no. 227 (January, 1999), pp. 1025-1055
  216. Wang, ZJ; Liu, JG; Childress, S, Connection between corner vortices and shear layer instability in flow past an ellipse, Physics of Fluids, vol. 11 no. 9 (January, 1999), pp. 2446-2448
  217. Choi, H; Liu, JG, The Reconstruction of Upwind Fluxes for Conservation Laws: Its Behavior in Dynamic and Steady State Calculations, Journal of Computational Physics, vol. 144 no. 2 (August, 1998), pp. 237-256, Elsevier BV
  218. Xu, E; Liu, JG, Pricing of mortgage-backed securities with option-adjusted spread, Managerial Finance, vol. 24 (1998), pp. 94-109
  219. E, W; Liu, JG, Finite Difference Methods for 3D Viscous Incompressible Flows in the Vorticity-Vector Potential Formulation on Nonstaggered Grids, Journal of Computational Physics, vol. 138 no. 1 (November, 1997), pp. 57-82, Elsevier BV
  220. Chen, GQ; Liu, JG, Convergence of difference schemes with high resolution for conservation laws, Mathematics of Computation, vol. 66 no. 219 (January, 1997), pp. 1027-1053
  221. Weinan, E; Liu, JG, Finite difference schemes for incompressible flows in the velocity - impulse density formulation, Journal of Computational Physics, vol. 130 no. 1 (January, 1997), pp. 67-76, Elsevier BV
  222. Weinan, E; Liu, JG, Vorticity boundary condition and related issues for finite difference schemes, Journal of Computational Physics, vol. 124 no. 2 (March, 1996), pp. 368-382, Elsevier BV
  223. Jin, S; Liu, JG, The effects of numerical viscosities: I. Slowly moving shocks, Journal of Computational Physics, vol. 126 no. 2 (January, 1996), pp. 373-389, Elsevier BV
  224. Weinan, E; Liu, JG, Essentially compact schemes for unsteady viscous incompressible flows, Journal of Computational Physics, vol. 126 no. 1 (January, 1996), pp. 122-138, Elsevier BV
  225. Weinan, E; Liu, JG, Projection method II: Godunov-Ryabenki analysis, SIAM Journal on Numerical Analysis, vol. 33 no. 4 (January, 1996), pp. 1597-1621, Society for Industrial & Applied Mathematics (SIAM)
  226. Levermore, CD; Liu, JG, Large oscillations arising in a dispersive numerical scheme, Physica D: Nonlinear Phenomena, vol. 99 no. 2-3 (January, 1996), pp. 191-216, Elsevier BV
  227. Liu, JG; Xin, Z, Kinetic and viscous boundary layers for broadwell equations, Transport Theory and Statistical Physics, vol. 25 no. 3-5 (January, 1996), pp. 447-461, Informa UK Limited
  228. Jin, S; Liu, JG, Oscillations induced by numerical viscosities, Mat. Contemp., vol. 10 (1996), pp. 169-180
  229. Liu, JG; Xin, Z, Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation, Arch. Rat. Mech. Anal., vol. 135 no. 1 (1996), pp. 61-105, Springer Nature
  230. E, W; Liu, J-G, Finite difference schemes for incompressible flows in vorticity formulations, edited by Gagnon, Y; Cottet, G-H; G., D; F., A; Meiburg, E, ESAIM: Proceedings, vol. 1 (1996), pp. 181-195, EDP Sciences
  231. Weinan, E; Liu, JG, Projection method I: convergence and numerical boundary layers, SIAM J. Numer. Anal., vol. 32 no. 4 (1995), pp. 1017-1057, Society for Industrial & Applied Mathematics (SIAM)
  232. Liu, JG; Xin, Z, Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheets data, Comm. Pure Appl. Math., vol. 48 no. 6 (1995), pp. 611-628
  233. Jin, S; Liu, JG, Relaxation and diffusion enhanced dispersive waves, Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences, vol. 446 no. 1928 (January, 1994), pp. 555-563
  234. Lefloch, P; Liu, JG, Discrete entropy and monotonicity criteria for hyperbolic conservation laws, C.R. Acad. Sci. Paris., vol. 319 no. 8 (1994), pp. 881-886, ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
  235. Chen, G-Q; Liu, J-G, Convergence of Second-Order Schemes for Isentropic Gas Dynamics, Mathematics of Computation, vol. 61 no. 204 (October, 1993), pp. 607-607, JSTOR
  236. Liu, JG; Xin, Z, Nonlinear stability of discrete shocks for systems of conservation laws, Archive for Rational Mechanics and Analysis, vol. 125 no. 3 (September, 1993), pp. 217-256, Springer Nature, ISSN 0003-9527
  237. Liu, J-G; Xin, Z, L 1 -Stability of Stationary Discrete Shocks, Mathematics of Computation, vol. 60 no. 201 (January, 1993), pp. 233-233, JSTOR
  238. Chen, GQ; Liu, JG, Convergence of second-order schemes for isentropic gas dynamics, Math. Comp., vol. 61 no. 204 (1993), pp. 607-629, AMER MATHEMATICAL SOC
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Papers Accepted

  1. 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. (2016)
  2. Y. Gao, J.-G. Liu, J. Lu, Continuum limit of a mesoscopic model of step motion on vicinal surfaces, J. Nonlinear Science (2016)