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Publications of Jian-Guo Liu    :chronological  alphabetical  combined  bibtex listing:

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, J-G; Xu, X, A note on one-dimensional time fractional ODEs, Applied Mathematics Letters, vol. 83 (September, 2018), pp. 87-94 [doi]
  2. Li, L; Liu, J-G; 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 [doi]  [abs]
  3. 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 [doi]  [abs]
  4. 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 [doi]
  5. 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) [doi]
  6. Liu, J-G; 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 [doi]  [abs]
  7. 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 [doi]  [abs]
  8. 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 [doi]  [abs]
  9. 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, SIAM PUBLICATIONS [doi]  [abs]
  10. Gao, Y; Li, L; Liu, J-G, A Dispersive Regularization for the Modified Camassa--Holm Equation, Siam Journal on Mathematical Analysis, vol. 50 no. 3 (January, 2018), pp. 2807-2838 [doi]
  11. Li, L; Liu, J-G, 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 [doi]
  12. Li, L; Liu, J-G; Lu, J, Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem, Journal of Statistical Physics, vol. 169 no. 2 (October, 2017), pp. 316-339 [doi]
  13. Liu, J-G; Wang, L; Zhou, Z, Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations, Mathematics of Computation, vol. 87 no. 311 (September, 2017), pp. 1165-1189 [doi]
  14. 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 [doi]
  15. 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 [doi]
  16. Gao, Y; Ji, H; Liu, J-G; 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 [doi]
  17. Gao, Y; Liu, J-G; 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 [doi]
  18. Gao, Y; Liu, J-G; 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 [doi]
  19. Liu, J-G; 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 [doi]
  20. Degond, P; Liu, J-G; Merino-Aceituno, S; Tardiveau, T, Continuum dynamics of the intention field under weakly cohesive social interaction, Mathematical Models & Methods in Applied Sciences, vol. 27 no. 01 (January, 2017), pp. 159-182 [doi]
  21. Gao, Y; Liu, J-G, 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 [doi]
  22. Liu, J-G; 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 [doi]
  23. Gao, Y; Ji, H; Liu, J-G; P. Witelski, T, A vicinal surface model for epitaxial growth with logarithmic free energy, Discrete & Continuous Dynamical Systems B, vol. 22 no. 11 (2017), pp. 1-21 [doi]
  24. Huang, H; Liu, J-G, Discrete-in-time random particle blob method for the Keller–Segel equation and convergence analysis, Communications in Mathematical Sciences, vol. 15 no. 7 (2017), pp. 1821-1842 [doi]  [abs]
  25. Degond, P; Herty, M; Liu, J-G, Mean-field games and model predictive control, Communications in Mathematical Sciences, vol. 15 no. 5 (2017), pp. 1403-1422 [doi]
  26. Li, L; Liu, J-G, A note on deconvolution with completely monotone sequences and discrete fractional calculus, Quarterly of Applied Mathematics (2017), pp. 1-1 [doi]
  27. Liu, J-G; Cong, W, Uniform $L^{\infty}$ boundedness for a degenerate parabolic-parabolic Keller-Segel model, Discrete and Continuous Dynamical Systems Series B, vol. 22 no. 2 (2017), pp. 307-338 [doi]
  28. Huang, H; Liu, J-G, A note on Monge–Ampère Keller–Segel equation, Applied Mathematics Letters, vol. 61 (November, 2016), pp. 26-34 [doi]
  29. 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 [doi]
  30. Liu, J-G; Huang, H, 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 (September, 2016), pp. 715-748 [doi]
  31. Liu, J-G; Cong, W, A degenerate $p$-Laplacian Keller-Segel model, Kinetic and Related Models, vol. 9 no. 4 (September, 2016), pp. 687-714 [doi]
  32. Liu, J-G; Wang, J, A Note on L ∞ $L^{\infty}$ -Bound and Uniqueness to a Degenerate Keller-Segel Model, Acta Applicandae Mathematicae, vol. 142 no. 1 (April, 2016), pp. 173-188, ISSN 0167-8019 [doi]
  33. Herschlag, G; Liu, J-G; 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, ISSN 1070-6631 [doi]
  34. Liu, J-G; Pego, RL, On generating functions of Hausdorff moment sequences, Transactions of the American Mathematical Society, vol. 368 no. 12 (February, 2016), pp. 8499-8518 [doi]
  35. Liu, J-G; Wang, J, Refined hyper-contractivity and uniqueness for the Keller–Segel equations, Applied Mathematics Letters, vol. 52 (2016), pp. 212-219 [doi]
  36. Chen, J; Liu, J-G; 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 [doi]
  37. Liu, J-G; Xu, X, Existence Theorems for a Multidimensional Crystal Surface Model, Siam Journal on Mathematical Analysis, vol. 48 no. 6 (January, 2016), pp. 3667-3687 [doi]
  38. 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, ISBN 9783319321424 [doi]  [abs]
  39. 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)
  40. 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
  41. 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
  42. Xue, Y; Wang, C; Liu, J-G, 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 (December, 2015), pp. 1189-1216, ISSN 0885-7474 [doi]
  43. Lu, J; Liu, J-G; 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 [doi]  [abs]
  44. 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, ISSN 0003-9527 [doi]  [abs]
  45. 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, ISSN 0168-9274 [doi]  [abs]
  46. Herschlag, G; Liu, J-G; 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, ISSN 0036-1399 [doi]
  47. 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 (October, 2014), pp. 20130394-20130394, ISSN 1364-503X [doi]
  48. Goudon, T; Jin, S; Liu, JG; 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, ISSN 0271-2091 [doi]  [abs]
  49. 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 (May, 2014), pp. 555-565, ISSN 0294-1449 [doi]  [abs]
  50. 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 (2014), pp. 1995-2011, ISSN 1078-0947 [doi]  [abs]
  51. 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 [doi]  [abs]
  52. Degond, P; Herty, M; Liu, J-G, Flow on Sweeping Networks, Multiscale Modeling & Simulation, vol. 12 no. 2 (January, 2014), pp. 538-565, ISSN 1540-3459 [doi]
  53. 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 [doi]  [abs]
  54. Chen, X; Li, X; Liu, J-G, 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 (2014), pp. 1579-1601, ISSN 1539-6746 [doi]
  55. 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, ISSN 0885-7474 [doi]  [abs]
  56. 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
  57. Zou, C; Liu, J-G; Bian, S, 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, ISSN 1937-5093 [doi]
  58. Huang, YL; Liu, JG; Wang, WC, A generalized mac scheme on curvilinear domains, Siam Journal on Scientific Computing, vol. 35 no. 5 (November, 2013), pp. B953-B986, ISSN 1064-8275 [doi]  [abs]
  59. 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
  60. 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
  61. 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, ISSN 0022-4715 [doi]  [abs]
  62. 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 [doi]  [abs]
  63. 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 [doi]  [abs]
  64. 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 (2013), pp. 1179-1215, ISSN 0036-1410 [doi]  [abs]
  65. Bian, S; Liu, J-G, 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, ISSN 0010-3616 [doi]  [abs]
  66. 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 (2013), pp. 145-164, ISSN 0021-9991 [doi]  [abs]
  67. Chen, X; Liu, J-G, 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 (2013), pp. 2764-2802, ISSN 0022-0396 [doi]  [abs]
  68. Haack, J; Jin, S; Liu, J, An All-Speed Asymptotic-Preserving Method for the Isentropic Euler and Navier-Stokes Equations, Communications in Computational Physics, vol. 12 no. 04 (October, 2012), pp. 955-980, ISSN 1815-2406 [doi]  [abs]
  69. Chen, L; Liu, J-G; Wang, J, Multidimensional Degenerate Keller–Segel System with Critical Diffusion Exponent $2n/(n+2)$, Siam Journal on Mathematical Analysis, vol. 44 no. 2 (January, 2012), pp. 1077-1102, ISSN 0036-1410 [doi]  [abs]
  70. 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
  71. Chae, D; Liu, J-G, Blow-up, Zero α Limit and the Liouville Type Theorem for the Euler-Poincaré Equations, Communications in Mathematical Physics, vol. 314 no. 3 (2012), pp. 671-687, ISSN 0010-3616 [doi]  [abs]
  72. Chen, X; Liu, J-G, Two nonlinear compactness theorems in L p(0,T;B), Applied Mathematics Letters, vol. 25 no. 12 (2012), pp. 2252-2257, ISSN 0893-9659 [doi]  [abs]
  73. Frouvelle, A; Liu, J-G, Dynamics in a kinetic model of oriented particles with phase transition, Siam Journal on Mathematical Analysis, vol. 44 no. 2 (2012), pp. 791-826, ISSN 0036-1410 [doi]  [abs]
  74. 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 (2012), pp. 43-55, ISSN 0167-8019 [doi]  [abs]
  75. Degond, P; Liu, J-G, Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation, Mathematical Models & Methods in Applied Sciences, vol. 22 no. SUPPL.1 (2012), pp. 1114001-18, ISSN 0218-2025 [doi]  [abs]
  76. Chertock, A; Liu, J-G; 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 (2012), pp. 1-21, ISSN 0036-1429 [doi]  [abs]
  77. 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. 1-30, ISSN 0938-8974 [doi]  [abs]
  78. Acheritogaray, M; Degond, P; Frouvelle, A; Liu, J-G, Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system, Kinetic and Related Models, vol. 4 no. 4 (November, 2011), pp. 901-918, ISSN 1937-5093 [doi]  [abs]
  79. Liu, J-G; Lorz, A, A coupled chemotaxis-fluid model: Global existence, Annales De L'Institut Henri Poincare (C) Non Linear Analysis, vol. 28 no. 5 (September, 2011), pp. 643-652, ISSN 0294-1449 [doi]  [abs]
  80. Jin, S; Liu, J-G; Wang, L, A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations, Math. Comp., vol. 82 (2013), pp. 749-779
  81. Zheng, W; Gao, H; Liu, J-G; 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 (2011), pp. 053411-8, ISSN 1050-2947 [doi]  [abs]
  82. Huang, Y-L; Liu, J-G; Wang, W-C, An FFT based fast poisson solver on spherical shells, Communications in Computational Physics, vol. 9 no. 3 (2011), pp. 649-667, ISSN 1815-2406 [doi]  [abs]
  83. Liu, J-G; 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, ISSN 0021-9991 [doi]  [abs]
  84. Liu, J-G; 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, ISSN 0036-1429 [repository], [doi]  [abs]
  85. 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  [abs]
  86. Liu, J-G; Pego, RL, Stable discretization of magnetohydrodynamics in bounded domains, Communications in Mathematical Sciences, vol. 8 no. 1 (2010), pp. 235-251, ISSN 1539-6746  [abs]
  87. Liu, J-G; 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 (2009), pp. 743-768, ISSN 0252-9599 [doi]  [abs]
  88. Liu, J-G; Wang, W-C, Characterization and regularity for axisymmetric solenoidal vector fields with application to navier-stokes equation, Siam Journal on Mathematical Analysis, vol. 41 no. 5 (2009), pp. 1825-1850, ISSN 0036-1410 [doi]  [abs]
  89. Ha, S-Y; Liu, J-G, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Communications in Mathematical Sciences, vol. 7 no. 2 (2009), pp. 297-325, ISSN 1539-6746 [doi]  [abs]
  90. 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
  91. Lin, P; Liu, J-G; 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, ISSN 1064-8275 [doi]  [abs]
  92. Liu, J-G; 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  [abs]
  93. Degond, P; Liu, J-G; Vignal, M-H, 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, ISSN 0036-1429 [doi]  [abs]
  94. Lu, X; Lin, P; Liu, J-G, Analysis of a sequential regularization method for the unsteady Navier-Stokes equations, Mathematics of Computation, vol. 77 no. 263 (2008), pp. 1467-1494, ISSN 0025-5718 [doi]  [abs]
  95. Liu, J-G; 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, ISSN 0010-3640 [doi]  [abs]
  96. 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.  [abs]
  97. 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
  98. 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  [abs]
  99. Antman, SS; Liu, J-G, Basic themes and pretty problems of nonlinear solid mechanics, Milan Journal of Mathematics, vol. 75 no. 1 (2007), pp. 135-176, ISSN 1424-9286 [doi]  [abs]
  100. 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.) [doi]  [abs]
  101. 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 [doi]  [abs]
  102. 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.
  103. Degond, P; Liu, J-G; Mieussens, L, Macroscopic fluid models with localized kinetic upscaling effects, Multiscale Modeling & Simulation, vol. 5 no. 3 (2006), pp. 940-979, ISSN 1540-3459 [doi]  [abs]
  104. Liu, J-G; Wang, W-C, 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, ISSN 0036-1429 [doi]  [abs]
  105. 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
  106. Li, B; Liu, J-G, Epitaxial Growth Without Slope Selection: Energetics, Coarsening, and Dynamic Scaling, Journal of Nonlinear Science, vol. 14 no. 5 (October, 2004), pp. 429-451, ISSN 0938-8974 [doi]  [abs]
  107. Johnston, H; Liu, J-G, 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 [doi]  [abs]
  108. Liu, J-G; Wang, W-C, 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 [doi]  [abs]
  109. Lin, H-E; Liu, J-G; Xu, W-Q, 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, ISSN 1534-0392  [abs]
  110. Liu, J-G; Xu, W-Q, Far field boundary condition for convection diffusion equation at zero viscosity limit, Quarterly of Applied Mathematics, vol. 62 no. 1 (2004), pp. 27-52  [abs]
  111. Wang, C; Liu, J-G; 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 [doi]  [abs]
  112. 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 [doi]  [abs]
  113. Ghil, M; Liu, J-G; 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, ISSN 0167-2789 [doi]  [abs]
  114. 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 [doi]  [abs]
  115. Liu, J-G; Wang, C, High order finite difference methods for unsteady incompressible flows in multi-connected domains, Computers and Fluids, vol. 33 no. 2 (2004), pp. 223-255 [doi]  [abs]
  116. LI, B; LIU, J-G, Thin film epitaxy with or without slope selection, European Journal of Applied Mathematics, vol. 14 no. 6 (2003), pp. 713-743 [doi]  [abs]
  117. 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 [doi]  [abs]
  118. 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
  119. Wang, C; Liu, J-G, 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  [abs]
  120. Chainais-Hillairet, C; Liu, J-G; Peng, Y-J, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis, Mathematical Modelling and Numerical Analysis, vol. 37 no. 2 (2003), pp. 319-338  [abs]
  121. 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 [doi]  [abs]
  122. Weinan, E; Liu, J-G, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317-332
  123. 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
  124. Johnston, H; Liu, J-G, Finite Difference Schemes for Incompressible Flow Based on Local Pressure Boundary Conditions, Journal of Computational Physics, vol. 180 no. 1 (2002), pp. 120-154, ISSN 0021-9991 [doi]  [abs]
  125. 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 [doi]  [abs]
  126. Weinan, E; Liu, J-G, Projection method III: Spatial discretization on the staggered grid, Mathematics of Computation, vol. 71 no. 237 (2002), pp. 27-47 [doi]  [abs]
  127. Liu, J-G; Xin, Z, Convergence of the point vortex method for 2-D vortex sheet, Mathematics of Computation, vol. 70 no. 234 (2001), pp. 595-606 [doi]  [abs]
  128. Liu, J-G; Weinan, E, Simple finite element method in vorticity formulation for incompressible flows, Mathematics of Computation, vol. 70 no. 234 (2001), pp. 579-593 [doi]  [abs]
  129. Liu, J-G; Wang, W-C, An energy-preserving MAC-Yee scheme for the incompressible MHD equation, Journal of Computational Physics, vol. 174 no. 1 (2001), pp. 12-37, ISSN 0021-9991 [doi]  [abs]
  130. Liu, J-G; Weinan, E, Simple finite element method in vorticity formulation for incompressible flow, Math. Comp., vol. 69 (2001), pp. 1385-1407
  131. 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 [doi]  [abs]
  132. 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, ISSN 0271-2091 [doi]  [abs]
  133. Liu, J-G; Shu, C-W, A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows, Journal of Computational Physics, vol. 160 no. 2 (2000), pp. 577-596 [doi]  [abs]
  134. 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 [doi]  [abs]
  135. Wang, C; Liu, J-G, Convergence of gauge method for incompressible flow, Mathematics of Computation, vol. 69 no. 232 (2000), pp. 1385-1407  [abs]
  136. Lefloch, PG; Liu, J-G, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions, Mathematics of Computation, vol. 68 no. 227 (1999), pp. 1025-1055  [abs]
  137. 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  [abs]
  138. Xu, E; Liu, J-G, Pricing of mortgage-backed securities with option-adjusted spread, Managerial Finance, vol. 24 (1998), pp. 94-109
  139. Choi, H; Liu, J-G, 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 [doi]  [abs]
  140. Weinan, E; Liu, J-G, 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 [doi]  [abs]
  141. Chen, G-Q; Liu, J-G, Convergence of difference schemes with high resolution for conservation laws, Mathematics of Computation, vol. 66 no. 219 (1997), pp. 1027-1053  [abs]
  142. Weinan, E; Liu, J-G, Finite difference schemes for incompressible flows in the velocity - impulse density formulation, Journal of Computational Physics, vol. 130 no. 1 (1997), pp. 67-76  [abs]
  143. Jin, S; Liu, J-G, Oscillations induced by numerical viscosities, Mat. Contemp., vol. 10 (1996), pp. 169-180
  144. Jin, S; Liu, J-G, The effects of numerical viscosities: I. Slowly moving shocks, Journal of Computational Physics, vol. 126 no. 2 (1996), pp. 373-389 [doi]  [abs]
  145. Weinan, E; Liu, J-G, Vorticity boundary condition and related issues for finite difference schemes, Journal of Computational Physics, vol. 124 no. 2 (1996), pp. 368-382 [doi]  [abs]
  146. Weinan, E; Liu, J-G, Essentially compact schemes for unsteady viscous incompressible flows, Journal of Computational Physics, vol. 126 no. 1 (1996), pp. 122-138 [doi]  [abs]
  147. Weinan, E; Liu, J-G, Projection method II: Godunov-Ryabenki analysis, SIAM Journal on Numerical Analysis, vol. 33 no. 4 (1996), pp. 1597-1621  [abs]
  148. Levermore, CD; Liu, J-G, Large oscillations arising in a dispersive numerical scheme, Physica D: Nonlinear Phenomena, vol. 99 no. 2-3 (1996), pp. 191-216  [abs]
  149. Liu, J-G; Xin, Z, Kinetic and viscous boundary layers for broadwell equations, Transport Theory and Statistical Physics, vol. 25 no. 3-5 (1996), pp. 447-461  [abs]
  150. Liu, J-G; Xin, Z, Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation, Arch. Rat. Mech. Anal., vol. 135 (1996), pp. 61-105
  151. Weinan, E; Liu, J-G, Projection method I: convergence and numerical boundary layers, SIAM J. Numer. Anal., vol. 32 (1995), pp. 1017-1057
  152. 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
  153. 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
  154. Jin, S; Liu, J-G, 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  [abs]
  155. Chen, G-Q; Liu, J-G, Convergence of second-order schemes for isentropic gas dynamics, Math. Comp., vol. 61 (1993), pp. 607-629
  156. Engquist, B; Liu, J-G, Numerical methods for oscillatory solutions to hyperbolic problems, Comm. Pure Appl. Math., vol. 46 (1993), pp. 1327-1361
  157. Liu, J-G; Xin, Z, L1-stability of stationary discrete shocks, Math. Comp., vol. 60 (1993), pp. 233-244
  158. Liu, J-G; 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, ISSN 0003-9527 [doi]  [abs]

Papers Accepted

  1. Degond, P; Liu, J-G; Pego, RL, Coagulation–Fragmentation Model for Animal Group-Size Statistics, Journal of Nonlinear Science, vol. 27 no. 2 (April, 2017), pp. 379-424 [doi]
  2. Huang, H; Liu, J-G, Error estimate of a random particle blob method for the Keller-Segel equation, Mathematics of Computation, vol. 86 no. 308 (February, 2017), pp. 2719-2744 [doi]
  3. Liu, J-G; Wang, J, Global existence for a thin film equation with subcritical mass, Discrete and Continuous Dynamical Systems Series B, vol. 22 no. 4 (February, 2017), pp. 1461-1492 [doi]
  4. Liu, J-G; Yang, R, A random particle blob method for the Keller-Segel equation and convergence analysis, Mathematics of Computation, vol. 86 no. 304 (May, 2016), pp. 725-745 [doi]
  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)

 

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