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. 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., Physics in Medicine and Biology, vol. 64 no. 2 (January, 2019), pp. 025007
  2. 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
  3. 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)
  4. 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)
  5. 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
  6. 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
  7. Liu, J-G; 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
  8. Chen, K; Li, Q; Liu, J-G, Online learning in optical tomography: a stochastic approach, Inverse Problems, vol. 34 no. 7 (July, 2018), pp. 075010-075010, IOP Publishing
  9. 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, Elsevier BV
  10. Gao, Y; Liu, J-G; 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
  11. Li, L; Liu, J-G, p -Euler equations and p -Navier–Stokes equations, Journal of Differential Equations, vol. 264 no. 7 (April, 2018), pp. 4707-4748, Elsevier BV
  12. 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
  13. Li, L; Liu, J-G, 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)
  14. 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)
  15. 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)
  16. 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)
  17. 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)
  18. 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
  19. Coquel, F; Jin, S; Liu, J-G; 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 (September, 2017), pp. 1083-1126, American Mathematical Society (AMS)
  20. Liu, J-G; 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
  21. 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
  22. 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
  23. 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 (2017), pp. 307-338, American Institute of Mathematical Sciences (AIMS)
  24. 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)
  25. Liu, JG; Wang, J, A generalized Sz. Nagy inequality in higher dimensions and the critical thin film equation, Nonlinearity, vol. 30 no. 1 (2017), pp. 35-60, IOP Publishing
  26. 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
  27. 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
  28. Degond, P; Liu, J-G; 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. 01 (January, 2017), pp. 159-182, World Scientific Pub Co Pte Lt
  29. 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)
  30. 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)
  31. Gao, Y; Liu, J-G, The modified Camassa-Holm equation in Lagrangian coordinates, Discrete & Continuous Dynamical Systems B, vol. 22 no. 11 (2017), pp. 1-48, American Institute of Mathematical Sciences (AIMS)
  32. Huang, H; Liu, JG, A note on Monge-Ampère Keller-Segel equation, Applied Mathematics Letters, vol. 61 (November, 2016), pp. 26-34, Elsevier BV
  33. Huang, H; Liu, J-G, Error estimates of the aggregation-diffusion splitting algorithms for the Keller-Segel equations, Discrete and Continuous Dynamical Systems Series B, vol. 21 no. 10 (November, 2016), pp. 3463-3478, American Institute of Mathematical Sciences (AIMS)
  34. 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
  35. 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
  36. Liu, J-G; Wang, J, Refined hyper-contractivity and uniqueness for the Keller–Segel equations, Applied Mathematics Letters, vol. 52 (2016), pp. 212-219, Elsevier BV
  37. Chen, J; Liu, JG; Zhou, Z, On a Schrödinger-Landau-Lifshitz system: Variational structure and numerical methods, Multiscale Modeling & Simulation, vol. 14 no. 4 (January, 2016), pp. 1463-1487, Society for Industrial & Applied Mathematics (SIAM)
  38. 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
  39. 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)
  40. 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)
  41. 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)
  42. 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
  43. J.-G. Liu and R. Yang, Propagation of chaos for large Brownian particle system with Coulomb interaction, Research in the Mathematical Sciences, vol. 3 no. 40 (2016)
  44. Y. Duan and J.-G. Liu, Error estimate of the particle method for the b-equation, Methods and Applications of Analysis, vol. 23 (2016), pp. 119-154
  45. J.-G. Liu and Y. Zhang, Convergence of stochastic interacting particle systems in probability under a Sobolev norm, Annals of Mathematical Sciences and Applications, vol. 1 (2016), pp. 251-299
  46. 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
  47. 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
  48. 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
  49. 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 (January, 2015), pp. 63-115
  50. 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
  51. 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. 20130394-20130394, The Royal Society, ISSN 1364-503X
  52. Degond, P; Frouvelle, A; Liu, J-G, Phase Transitions, Hysteresis, and Hyperbolicity for Self-Organized Alignment Dynamics, Archive for Rational Mechanics and Analysis, vol. 216 no. 1 (October, 2014), pp. 63-115, Springer New York LLC, ISSN 0003-9527
  53. 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 (May, 2014), pp. 81-102, WILEY, ISSN 0271-2091
  54. 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 (2014), pp. 9-28, American Institute of Mathematical Sciences (AIMS), ISSN 1937-5093
  55. 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 (February, 2014), pp. 751-780, Springer Nature, ISSN 0022-4715
  56. 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 (January, 2014), pp. 1051-1084, ISSN 0003-9527
  57. Degond, P; Herty, M; Liu, JG, Flow on sweeping networks, Multiscale Modeling & Simulation, vol. 12 no. 2 (January, 2014), pp. 538-565, Society for Industrial & Applied Mathematics (SIAM), ISSN 1540-3459
  58. 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
  59. Chae, D; Degond, P; Liu, JG, Well-posedness for hall-magnetohydrodynamics, Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 31 no. 3 (January, 2014), pp. 555-565
  60. Johnston, H; Wang, C; Liu, J-G, A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier–Stokes Equations, Journal of Scientific Computing, vol. 60 no. 3 (2014), pp. 612-626, Springer Nature, ISSN 0885-7474
  61. 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, HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, vol. 8 (2014), pp. 179-192
  62. Duan, Y; Liu, J-G, Convergence analysis of the vortex blob method for the $b$-equation, Discrete and Continuous Dynamical Systems Series A, vol. 34 no. 5 (2014), pp. 1995-2011, American Institute of Mathematical Sciences (AIMS), ISSN 1078-0947
  63. Goudon, T; Jin, S; Liu, J-G; 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
  64. Degond, P; Frouvelle, A; Liu, JG, Macroscopic limits and phase transition in a system of self-propelled particles, Journal of Nonlinear Science, vol. 23 no. 3 (2013), pp. 427-456, Springer Nature, ISSN 0938-8974
  65. 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
  66. Jin, S; Liu, JG; Wang, L, A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations, Mathematics of Computation, vol. 82 no. 282 (2013), pp. 749-779, American Mathematical Society (AMS)
  67. Huang, Y-L; Liu, J-G; Wang, W-C, 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
  68. Chen, X; Liu, J-G, Analysis of Polymeric Flow Models and Related Compactness Theorems in Weighted Spaces, Siam Journal on Mathematical Analysis, vol. 45 no. 3 (January, 2013), pp. 1179-1215, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  69. 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, vol. 2012 - 2013 (2013), pp. 1-27
  70. P. Degond, J.-G, Liu, S. Motsch, V. Panferov, Hydrodynamic models of self-organized dynamics: derivation and existence theory, Methods Anal. Appl., vol. 20 (2013), pp. 89-114
  71. 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
  72. 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
  73. Chae, D; Degond, P; Liu, J-G, Well-posedness for Hall-magnetohydrodynamics, Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 31 no. 3 (2013), pp. 555-565, Elsevier BV, ISSN 0294-1449
  74. 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 (2013), pp. 1-54, Springer Nature, ISSN 0010-3616
  75. Degond, P; Frouvelle, A; Liu, J-G, Macroscopic limits and phase transition in a system of self-propelled particles, Journal of Nonlinear Science, vol. 23 no. 3 (2013), pp. 427-456
  76. Haack, J; Jin, S; Liu, JG, An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations, Communications in Computational Physics, vol. 12 no. 4 (October, 2012), pp. 955-980, Global Science Press, ISSN 1815-2406
  77. Chae, D; Liu, JG, Blow-up, Zero α Limit and the Liouville Type Theorem for the Euler-Poincaré Equations, Communications in Mathematical Physics, vol. 314 no. 3 (September, 2012), pp. 671-687, Springer Nature, ISSN 0010-3616
  78. Carrillo, JA; Chen, L; Liu, J-G; Wang, J, A Note on the Subcritical Two Dimensional Keller-Segel System, Acta Applicandae Mathematicae, vol. 119 no. 1 (June, 2012), pp. 43-55, Springer Nature, ISSN 0167-8019
  79. Chen, L; Liu, JG; Wang, J, Multidimensional degenerate Keller-Segel system with critical diffusion exponent 2n/(n + 2), Siam Journal on Mathematical Analysis, vol. 44 no. 2 (May, 2012), pp. 1077-1102, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  80. Frouvelle, A; Liu, JG, Dynamics in a kinetic model of oriented particles with phase transition, Siam Journal on Mathematical Analysis, vol. 44 no. 2 (May, 2012), pp. 791-826, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  81. Chertock, A; Liu, JG; Pendleton, T, Convergence of a particle method and global weak solutions of a family of evolutionary PDEs, Siam Journal on Numerical Analysis, vol. 50 no. 1 (May, 2012), pp. 1-21, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  82. DEGOND, PIERRE; LIU, JIAN-GUO, HYDRODYNAMICS OF SELF-ALIGNMENT INTERACTIONS WITH PRECESSION AND DERIVATION OF THE LANDAU–LIFSCHITZ–GILBERT EQUATION, Mathematical Models and Methods in Applied Sciences, vol. 22 no. supp01 (April, 2012), pp. 1140001-1140001, World Scientific Pub Co Pte Lt, ISSN 0218-2025
  83. Chen, X; Liu, JG, Two nonlinear compactness theorems in Lp(0,T;B), Applied Mathematics Letters, vol. 25 no. 12 (January, 2012), pp. 2252-2257, Elsevier BV, ISSN 0893-9659
  84. 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
  85. 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 (December, 2011), pp. 901-918, American Institute of Mathematical Sciences (AIMS), ISSN 1937-5093
  86. 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, vol. 84 no. 5 (November, 2011), pp. 053411-8, American Physical Society (APS), ISSN 1050-2947
  87. Huang, YL; Liu, JG; Wang, WC, An FFT based fast poisson solver on spherical shells, Communications in Computational Physics, vol. 9 no. 3 (2011), pp. 649-667, Global Science Press, ISSN 1815-2406
  88. Liu, JG; Lorz, A, A coupled chemotaxis-fluid model: Global existence, Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 28 no. 5 (January, 2011), pp. 643-652, Elsevier BV, ISSN 0294-1449
  89. Liu, JG; Liu, J; Pego, RL, Stable and accurate pressure approximation for unsteady incompressible viscous flow, Journal of Computational Physics, vol. 229 no. 9 (May, 2010), pp. 3428-3453, Elsevier BV, ISSN 0021-9991
  90. Liu, JG; Mieussens, L, Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit, Siam Journal on Numerical Analysis, vol. 48 no. 4 (January, 2010), pp. 1474-1491, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  91. 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
  92. Liu, J-G; Pego, R, Stable discretization of magnetohydrodynamics in bounded domains, Commun. Math. Sci., vol. 8 no. 1 (2010), pp. 234-251, ISSN 1539-6746
  93. 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
  94. Liu, JG; Wang, WC, Characterization and regularity for axisymmetric solenoidal vector fields with application to navier-stokes equation, Siam Journal on Mathematical Analysis, vol. 41 no. 5 (December, 2009), pp. 1825-1850, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  95. Ha, SY; Liu, JG, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Communications in Mathematical Sciences, vol. 7 no. 2 (January, 2009), pp. 297-325, International Press of Boston, ISSN 1539-6746
  96. 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 (2008), pp. 1298-1322, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  97. 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 (2008), pp. 398-419, Society for Industrial & Applied Mathematics (SIAM), ISSN 1064-8275
  98. 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 (2008), pp. 26-55, ISSN 1815-2406
  99. 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 (2008), pp. 1467-1494, American Mathematical Society (AMS), ISSN 0025-5718
  100. Hsia, C-H; Liu, J-G; Wang, C, Structural stability and bifurcation for 2D incompressible ows with symmetry, Meth. Appl. Anal., vol. 15 (2008), pp. 495-512
  101. 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
  102. 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
  103. 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.
  104. Liu, J-G; 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
  105. 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
  106. Moore, J; Cheng, Z; Hao, J; Guo, G; Liu, J-G; Lin, C; Yu, L, 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 (2007), pp. 10173-10182, ISSN 0021-8561 (published on Web 10/30/2007.)
  107. Degond, P; Liu, JG; Mieussens, L, Macroscopic fluid models with localized kinetic upscaling effects, Multiscale Modeling & Simulation, vol. 5 no. 3 (2006), pp. 940-979, Society for Industrial & Applied Mathematics (SIAM), ISSN 1540-3459
  108. 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 (2006), pp. 5313-5322, ISSN 0021-8561
  109. 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 (2006), pp. 2456-2480, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  110. 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.
  111. Liu, J-G; Samelson, R; Wang, C, Global weak solution of planetary geostrophic equations with inviscid geostrophic balance, Applicable Analysis, vol. 85 (2006), pp. 593-605
  112. 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 (2004), pp. 8-33, Elsevier BV
  113. 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 (2004), pp. 149-173, Elsevier BV, ISSN 0167-2789
  114. 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
  115. 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 (2004), pp. 221-259, Elsevier BV
  116. 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 (2004), pp. 267-290, American Institute of Mathematical Sciences (AIMS), ISSN 1534-0392
  117. 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 (2004), pp. 555-594, Springer Nature
  118. Liu, JG; Xu, WQ, Far field boundary condition for convection diffusion equation at zero viscosity limit, Quarterly of Applied Mathematics, vol. 62 no. 1 (2004), pp. 27-52, American Mathematical Society (AMS)
  119. Liu, JG; Wang, C, High order finite difference methods for unsteady incompressible flows in multi-connected domains, Computers & Fluids, vol. 33 no. 2 (January, 2004), pp. 223-255, Elsevier BV
  120. Li, B; Liu, J-G, Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling, J. Nonlinear Sci., vol. 14 no. 5 (2004), pp. 429-451, ISSN 0938-8974
  121. Liu, J-G; 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
  122. LI, BO; LIU, JIAN-GUO, Thin film epitaxy with or without slope selection, European Journal of Applied Mathematics, vol. 14 no. 6 (2003), pp. 713-743, Cambridge University Press (CUP)
  123. 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 (2003), pp. 201-228, American Institute of Mathematical Sciences (AIMS)
  124. Liu, JG; Wang, C; Johnston, H, A Fourth Order Scheme for Incompressible Boussinesq Equations, Journal of Scientific Computing, vol. 18 no. 2 (2003), pp. 253-285, ISSN 0885-7474
  125. Chainais-Hillairet, C; Liu, JG; Peng, YJ, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis, Esaim: Mathematical Modelling and Numerical Analysis, vol. 37 no. 2 (2003), pp. 319-338, E D P SCIENCES
  126. Wang, C; Liu, J-G, Fourth order convergence of a compact difference solver for incompressible flow, Commun. Appl. Anal., vol. 7 (2003), pp. 171-191
  127. Duraisamy, K; Baeder, JD; Liu, J-G, Concepts and Application of Time-Limiters to High Resolution Schemes, Journal of Scientific Computing, vol. 19 no. 1-3 (2003), pp. 139-162, ISSN 0885-7474
  128. Weinan, E; Liu, J-G, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317-332
  129. Chern, I-L; Liu, J-G; Wang, W-C, Accurate evaluation of electrostatics for macromolecules in solution, Methods and Applications of Analysis, vol. 10 (2003), pp. 309-328
  130. Johnston, H; Liu, JG, Finite difference schemes for incompressible flow based on local pressure boundary conditions, Journal of Computational Physics, vol. 180 no. 1 (2002), pp. 120-154, Elsevier BV, ISSN 0021-9991
  131. Weinan, E; Liu, JG, Projection method III: Spatial discretization on the staggered grid, Mathematics of Computation, vol. 71 no. 237 (2002), pp. 27-47, American Mathematical Society (AMS)
  132. Wang, C; Liu, J-G, Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation, Numerische Mathematik, vol. 91 no. 3 (2002), pp. 543-576
  133. Liu, JG; Wang, WC, An energy-preserving MAC-Yee scheme for the incompressible MHD equation, Journal of Computational Physics, vol. 174 no. 1 (2001), pp. 12-37, Elsevier BV, ISSN 0021-9991
  134. 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)
  135. Liu, J-G; Weinan, E, Simple finite element method in vorticity formulation for incompressible flow, Math. Comp., vol. 69 (2001), pp. 1385-1407
  136. Liu, J-G; Xin, Z, Convergence of point vortex method for 2-D vortex sheet, Math. Comp., vol. 70 no. 234 (2001), pp. 565-606
  137. Weinan, E; Liu, JG, Gauge finite element method for incompressible flows, International Journal for Numerical Methods in Fluids, vol. 34 no. 8 (2000), pp. 701-710, WILEY, ISSN 0271-2091
  138. Wang, C; Liu, JG, Convergence of gauge method for incompressible flow, Mathematics of Computation, vol. 69 no. 232 (2000), pp. 1385-1407
  139. Liu, JG; Shu, CW, A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows, Journal of Computational Physics, vol. 160 no. 2 (2000), pp. 577-596, Elsevier BV
  140. Liu, J-G; Xin, Z, Convergence of the point vortex method for 2-D vortex sheet, Mathematics of Computation, vol. 70 no. 234 (April, 2000), pp. 595-607, American Mathematical Society (AMS)
  141. 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 (2000), pp. 786-798, WILEY
  142. Lefloch, PG; Liu, JG, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions, Mathematics of Computation, vol. 68 no. 227 (1999), pp. 1025-1055
  143. 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 (1999), pp. 2446-2448
  144. 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 (1998), pp. 237-256, Elsevier BV
  145. Xu, E; Liu, J-G, Pricing of mortgage-backed securities with option-adjusted spread, Managerial Finance, vol. 24 (1998), pp. 94-109
  146. 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 (1997), pp. 57-82, Elsevier BV
  147. Chen, GQ; Liu, JG, Convergence of difference schemes with high resolution for conservation laws, Mathematics of Computation, vol. 66 no. 219 (1997), pp. 1027-1053
  148. Weinan, E; Liu, JG, Finite difference schemes for incompressible flows in the velocity - impulse density formulation, Journal of Computational Physics, vol. 130 no. 1 (1997), pp. 67-76, Elsevier BV
  149. Liu, JG; Xin, Z, Boundary-layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation, Archive for Rational Mechanics and Analysis, vol. 135 no. 1 (1996), pp. 61-105, Springer Nature
  150. Weinan, E; Liu, JG, Projection method II: Godunov-Ryabenki analysis, Siam Journal on Numerical Analysis, vol. 33 no. 4 (1996), pp. 1597-1621, Society for Industrial & Applied Mathematics (SIAM)
  151. Weinan, E; Liu, JG, Vorticity boundary condition and related issues for finite difference schemes, Journal of Computational Physics, vol. 124 no. 2 (1996), pp. 368-382, Elsevier BV
  152. Jin, S; Liu, JG, The effects of numerical viscosities: I. Slowly moving shocks, Journal of Computational Physics, vol. 126 no. 2 (1996), pp. 373-389, Elsevier BV
  153. Weinan, E; Liu, JG, Essentially compact schemes for unsteady viscous incompressible flows, Journal of Computational Physics, vol. 126 no. 1 (1996), pp. 122-138, Elsevier BV
  154. Levermore, CD; Liu, JG, Large oscillations arising in a dispersive numerical scheme, Physica D: Nonlinear Phenomena, vol. 99 no. 2-3 (1996), pp. 191-216, Elsevier BV
  155. Liu, JG; Xin, Z, Kinetic and viscous boundary layers for broadwell equations, Transport Theory and Statistical Physics, vol. 25 no. 3-5 (1996), pp. 447-461, Informa UK Limited
  156. Jin, S; Liu, J-G, Oscillations induced by numerical viscosities, Mat. Contemp., vol. 10 (1996), pp. 169-180
  157. Weinan, E; Liu, J-G, Projection method I: convergence and numerical boundary layers, SIAM J. Numer. Anal., vol. 32 (1995), pp. 1017-1057
  158. Liu, J-G; 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 (1995), pp. 611-628
  159. Lefloch, P; Liu, J-G, Discrete entropy and monotonicity criteria for hyperbolic conservation laws, C.R. Acad. Sci. Paris., vol. 319 (1994), pp. 881-886
  160. 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 (1994), pp. 555-563
  161. Liu, JG; Xin, Z, Nonlinear stability of discrete shocks for systems of conservation laws, Archive for Rational Mechanics and Analysis, vol. 125 no. 3 (1993), pp. 217-256, Springer Nature, ISSN 0003-9527
  162. Chen, GQ; Liu, JG, Convergence of second-order schemes for isentropic gas dynamics, Mathematics of Computation, vol. 61 no. 204 (1993), pp. 607-627, American Mathematical Society (AMS)
  163. Engquist, B; Liu, J, Numerical methods for oscillatory solutions to hyperbolic problems, Communications on Pure and Applied Mathematics, vol. 46 no. 10 (1993), pp. 1327-1361, WILEY
  164. Liu, JG; Xin, Z, L1-stability of stationary discrete shocks, Mathematics of Computation, vol. 60 no. 201 (1993), pp. 233-244, American Mathematical Society (AMS)

Papers Accepted

  1. 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)
  2. 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
  3. 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)
  4. 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)
  5. 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)
  6. Y. Gao, J.-G. Liu, J. Lu, Continuum limit of a mesoscopic model of step motion on vicinal surfaces, J. Nonlinear Science (2016)