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Publications of Jian-Guo Liu    :chronological  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. W. Zheng, H. Gao, J.-G.-Liu, Y. Zhang, Q. Ye and C. Swank, General solution to gradient-induced transverse and longitudinal relaxation of spins undergoing restricted diffusion, Phys. Rev. A, vol. 84 (2011), pp. 053411-8
  2. M. Acheritogaray, P. Degond, A. Frouvelle, and J.-G. Liu, Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system, Kinetic and Related Models, vol. 4 (2011), pp. 901-918
  3. J.-G. Liu and A. Lorz, A coupled chemotaxis-fluid model: Global existence, Ann. I. H. Poincare, AN, vol. 28 (2011), pp. 643-652
  4. Y.-L. Huang, J.-G. Liu and W.-C. Wang, An FFT based fast Poisson solver on spherical shells, Commun. Comput. Phy., vol. 9 (2011), pp. 649-667  [abs]
  5. J.-G. Liu, Jie Liu and R. Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow, J. Comput. Phys., vol. 229 (2010), pp. 3428-3453
  6. J.-G. Liu and L. Mieussens, Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit, SIAM J. Numer. Anal., vol. 48 (2010), pp. 1474-1491  [abs]
  7. J.-G. Liu and R. Pego, Stable discretization of magnetohydrodynamics in bounded domains, Commun. Math. Sci., vol. 8 (2010), pp. 234-251
  8. S.-Y. Ha and J.-G. Liu, A simple proof of the Cucker-Smale flocking dynamics and mean-field limit, Commun. Math. Sci., vol. 7 (2009), pp. 297-325
  9. J.-G. Liu and W.-C. Wang, Characterization and regularity for axisymmetric solenoidal vector elds with application to Navier-Stokes equation, SIAM J. Math. Anal., vol. 41 (2009), pp. 1825-1850
  10. J.-G. Liu, J. Liu and R. Pego, Error estimates for finite-element Navier-Stokes solvers without standard inf-sup conditions, Chin. Ann. Math. Ser. B, vol. 30 (2009), pp. 743-768
  11. X. Lu, P. Lin and J.-G. Liu, Analysis of a sequential regularization method for the unsteady Navier-Stokes equations, Math. Comp., vol. 77 (2008), pp. 1467-1494  [abs]
  12. P. Degond, J.-G. Liu and M.H. Vignal, Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit, SIAM J. Num. Anal., vol. 46 (2008), pp. 1298-1322  [abs]
  13. J.-G. Liu and C. Wang, A fourth order numerical method for the primitive equations formulated in mean vorticity, Commun. Comput. Phys., vol. 4 (2008), pp. 26-55
  14. P. Lin, J.-G. Liu and X. Lu, Long time numerical solutyion of the Navier-Stokes equations based on a sequential regularization formulation, SIAM J. Sci. Comput., vol. 31 (2008), pp. 398-419
  15. C.-H. Hsia, J.-G. Liu and C. Wang, Structural stability and bifurcation for 2D incompressible ows with symmetry, Meth. Appl. Anal., vol. 15 (2008), pp. 495-512
  16. 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]
  17. J. Moore, Z. Cheng, J. Hao, G. Guo, J.-G. Liu, C. Lin and L. Yu, Effects of solid-state yeast treatment on the antioxidant properties and protein and fiber compositions of common hard wheat bran, J Agric Food Chem (2007) (published on Web 10/30/2007.)
  18. S.S. Antman and J.-G. Liu, Basic themes and pretty problems of nonlinear solid mechanics, Milan J. Math., vol. 75 (2007), pp. 135-176  [abs]
  19. J.-G. Liu, J. Liu and R. Pego, 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
  20. P. Degond, S. Jin, and J.G. Liu, Mach-number uniform asymptotic- preserving Gauge schemes for compressible flows, Bulletin of the Institute of Mathematics Academia Sinica (New Series), vol. 2 (2007), pp. 851-892  [abs]
  21. J.-G. Liu, R. Samelson and C. Wang, Global weak solution of planetary geostrophic equations with inviscid geostrophic balance, Applicable Analysis, vol. 85 (2006), pp. 593 - 605
  22. J.-G. Liu and W.C. Wang, Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows, SIAM J. Numer. Anal., vol. 44 (2006), pp. 2456-2480  [abs]
  23. P. Degond, J.-G. Liu, and L. Mieussens, Macroscopic fluid models with localized kinetic upscaling effects, Multiscale Model. Simul., vol. 5 (2006), pp. 940--979
  24. 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.
  25. J. Moore, J.-G. Liu, K. Zhou, S. Haley, and L. Yu, Effects of genotype and environment on the antioxidant properties of hard winter wheat bran, J Agric Food Chem, vol. 54 (2006), pp. 5313-5322
  26. J.-G. Liu and C. Wang, High order finite difference method for unsteady incompressible flow on multi-connected domain in vorticity-stream function formulation, Computer and Fluids, vol. 33 (2004), pp. 223-255
  27. M. Ghil, J.-G. Liu, C. Wang and S. Wang, Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow, Physica D, vol. 197 (2004), pp. 149--173
  28. H. Johnston and J.-G. Liu, Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term, J. Comput. Phys., vol. 188 (2004), pp. 221-259
  29. J.-G. Liu and W.-C. Wang, Energy and helicity preserving schemes for hydro- and magneto-hydrodynamics flows with symmetry, J. Comput. Phys., vol. 200 (2004), pp. 8-33
  30. B. Li and J.-G. Liu, Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling, J. Nonlinear Sci., vol. 14 (2004), pp. 429--451
  31. C. Wang, J.-G. Liu and H. Johnston, Analysis of a fourth order finite difference method for the incompressible Boussinesq equations, Numer. Math., vol. 97 (2004), pp. 555--594
  32. J.-G. Liu, and W.-Q. Xu, Far field boundary condition for convection diffusion equation at zero viscosity limit, Q APPL MATH, vol. 62 (2004), pp. 27-52
  33. H.-E. Lin, J.-G. Liu, and W.-Q. Xu, Effects of small viscosity and far field boundary conditions for hyperbolic systems, Comm. Pure Applied Anal., vol. 3 (2004), pp. 267-290
  34. J.-G. Liu, C. Wang and H. Johnston, A fourth order compact scheme for incompressible Boussinesq equations, J. Sci. Comput., vol. 18 (2003), pp. 253-285
  35. I.-L. Chern, J.-G. Liu and W.-C. Wang, Accurate evaluation of electrostatics for macromolecules in solution, Methods and Applications of Analysis, vol. 10 (2003), pp. 309-328
  36. B. Li and J.-G. Liu, Thin film epitaxy with or without slope selection, European J. Applied Math., vol. 14 (2003), pp. 713-743
  37. Weinan E and J.-G. Liu, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317--332
  38. K. Duraisamy, J.D. Baeder and J.-G. Liu, Concepts and application of time limiters to high resolution schemes, J. Sci. Comput., vol. 19 (2003), pp. 139-162
  39. C. Chainais-Hillairet, J.-G. Liu and Y.-J. Peng, Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis, Math. Model. Numer. Anal., vol. 37 (2003), pp. 319-338
  40. C. Wang and J.-G. Liu, Positivity property of second-order flux-splitting schemes for the compressible Euler equations, Discrete Contin. Dyn. Syst. Ser. B., vol. 3 (2003), pp. 201-228
  41. C. Wang and J.-G. Liu, Fourth order convergence of a compact difference solver for incompressible flow, Commun. Appl. Anal., vol. 7 (2003), pp. 171-191
  42. H. Johnston and J.-G. Liu, Finite difference schemes for incompressible flow based on local pressure boundary condition, J. Comput. Phys., vol. 180 (2002), pp. 120-154
  43. Weinan E and J.-G. Liu, Projection method III: spatial discretization on the staggered grid, Math. Comp., vol. 71 (2002), pp. 27-47
  44. C. Wang and J.-G. Liu, Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation, Numer. Math., vol. 91 (2002), pp. 543-576
  45. J.-G. Liu and Z. Xin, Convergence of point vortex method for 2-D vortex sheet, Math. Comp., vol. 70 (2001), pp. 565-606
  46. J.-G. Liu and Weinan E, Simple finite element method in vorticity formulation for incompressible flow, Math. Comp., vol. 69 (2001), pp. 1385-1407
  47. J.-G. Liu and W.C. Wang, An energy preserving MAC-Yee scheme for the incompressible MHD equation, J. Comput. Phys., vol. 174 (2001), pp. 12-37
  48. Weinan E and J.-G. Liu, Gauge finite element method for incompressible flows, Int. J. Num. Meth. Fluids, vol. 34 (2000), pp. 701-710
  49. C. Wang and J.-G. Liu, Convergence of gauge method for incompressible flow, Math. Comp., vol. 69 (2000), pp. 1385-1407
  50. J.-G. Liu and C.-W. Shu, A high order discontinuous Galerkin method for incompressible flows, J. Comput. Phys., vol. 160 (2000), pp. 577-596
  51. J.-G. Liu and Z. Xin, Convergence of a Galerkin method for 2-D discontinuous Euler flows, Comm. Pure Appl. Math., vol. 53 (2000), pp. 786-798
  52. Z.J. Wang, S. Childress and J.-G. Liu, Connection between corner vortices and shear layer instability in flow past an ellipse, Phys. Fluids., vol. 11 (1999), pp. 2446-2448
  53. P. Lefloch and J.-G. Liu, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions, Math. Comp., vol. 68 (1999), pp. 1025-1055
  54. H. Choi and J.-G. Liu, The reconstruction of upwind fluxes for conservation laws, its behavior in dynamic and steady state calculations, J. Comput. Phys., vol. 144 (1998), pp. 237-256
  55. E. Xu and J.-G. Liu, Pricing of mortgage-backed securities with option-adjusted spread, Managerial Finance, vol. 24 (1998), pp. 94-109
  56. Weinan E and J.-G. Liu, Finite difference schemes for incompressible flows in the impulse-velocity formulation, J. Comput. Phys., vol. 130 (1997), pp. 67-76
  57. G.-Q. Chen and J.-G. Liu, Convergence of difference schemes with high resolutions to conservation laws, Math. Comp., vol. 66 (1997), pp. 1027-1053
  58. Weinan E and J.-G. Liu, Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on non-staggered grids, J. Comput. Phys., vol. 138 (1997), pp. 57-82
  59. J.-G. Liu and Z. Xin, Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation, Arch. Rat. Mech. Anal., vol. 135 (1996), pp. 61-105
  60. J.-G. Liu and Z. Xin, Kinetic and viscous boundary layers for the Broadwell equations, Transport Theory Statist. Phys., vol. 25 (1996), pp. 447-461
  61. C.D. Levermore and J.-G. Liu, Large oscillations arising from a dispersive numerical scheme, Physica D, vol. 99 (1996), pp. 191-216
  62. Weinan E and J.-G. Liu, Projection method II: Godunov-Ryabenki analysis, SIAM J. Numer. Anal., vol. 33 (1996), pp. 1597-1621
  63. Weinan E and J.-G. Liu, Essential compact scheme for unsteady viscous incompressible flows, J. Comput. Phys., vol. 126 (1996), pp. 122-138
  64. Weinan E and J.-G. Liu, Vorticity boundary condition and related issues for finite difference schemes, J. Comput. Phys., vol. 124 (1996), pp. 368-382
  65. S. Jin and J.-G. Liu, The effects of numerical viscosities I: slowly moving shocks, J. Comput. Phys., vol. 126 (1996), pp. 373-389
  66. S. Jin and J.-G. Liu, Oscillations induced by numerical viscosities, Mat. Contemp., vol. 10 (1996), pp. 169-180
  67. J.-G. Liu and Z. Xin, Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheets data, Comm. Pure Appl. Math., vol. 48 (1995), pp. 611-628
  68. Weinan E and J.-G. Liu, Projection method I: convergence and numerical boundary layers, SIAM J. Numer. Anal., vol. 32 (1995), pp. 1017-1057
  69. S. Jin and J.-G. Liu, Relaxation and diffusion enhanced dispersive waves, Proc. Roy. Soc. Lon. Ser. A, vol. 446 (1994), pp. 555-563
  70. P. Lefloch and J.-G. Liu, Discrete entropy and monotonicity criteria for hyperbolic conservation laws, C.R. Acad. Sci. Paris., vol. 319 (1994), pp. 881-886
  71. J.-G. Liu and Z. Xin, Nonlinear stability of discrete shocks for systems of conservation laws, Arch. Rat. Mech. Anal., vol. 125 (1993), pp. 217-256
  72. J.-G. Liu and Z. Xin, L1-stability of stationary discrete shocks, Math. Comp., vol. 60 (1993), pp. 233-244
  73. B. Engquist and J.-G. Liu, Numerical methods for oscillatory solutions to hyperbolic problems, Comm. Pure Appl. Math., vol. 46 (1993), pp. 1327-1361
  74. G.-Q. Chen and J.-G. Liu, Convergence of second-order schemes for isentropic gas dynamics, Math. Comp., vol. 61 (1993), pp. 607-629

Papers Accepted

  1. J. Haack, S. Jin and J.-G. Liu, An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations, Commun. Comput. Phy. (2011)
  2. 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" (2011)
  3. A. Chertock, J.-G. Liu, and T. Pendleton, Convergence of a particle method and global weak solutions of a family of evolutionary PDEs, SIAM Numer. Anal. (2011)
  4. P. Degond and J.-G. Liu, Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation, Math. Models Methods Appl. Sci. (2011)
  5. S. Jin, J.-G. Liu and L. Wang, A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations, Math. Comp. (2011)
  6. J. Carrillo, L. Chen, J.-G. Liu and J. Wang, A Note on the Subcritical Two Dimensional Keller-Segel System, Acta Applicanda Mathematicae (2011)