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 .
  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 .
  3. Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization, edited by W. Bao and J.-G. Liu (2007), World Scientific .
Papers Published
  1. 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 .
  2. 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 .
  3. 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 .
  4. 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] .
  5. 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] .
  6. 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 .
  7. 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 .
  8. 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 .
  9. 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] .
  10. 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.) .
  11. 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] .
  12. 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 [abs] .
  13. 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] .
  14. 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 .
  15. 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] .
  16. 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 [abs] .
  17. 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. .
  18. 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 .
  19. 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 .
  20. 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 .
  21. 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 .
  22. J.-G. Liu and W.-C. Wang, Energy and helicity preserving finite difference schemes for ows with symmetry, J. Comput. Phys., vol. 200 (2004), pp. 8-33 .
  23. 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 .
  24. 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 .
  25. 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 .
  26. 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 .
  27. 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 .
  28. 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 .
  29. B. Li and J.-G. Liu, Thin film epitaxy with or without slope selection, European J. Applied Math., vol. 14 (2003), pp. 713-743 .
  30. Weinan E and J.-G. Liu, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317--332 .
  31. 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 .
  32. 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 .
  33. 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 .
  34. 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 .
  35. 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 .
  36. Weinan E and J.-G. Liu, Projection method III: spatial discretization on the staggered grid, Math. Comp., vol. 71 (2002), pp. 27-47 .
  37. 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 .
  38. J.-G. Liu and Z. Xin, Convergence of point vortex method for 2-D vortex sheet, Math. Comp., vol. 70 (2001), pp. 565-606 .
  39. J.-G. Liu and Weinan E, Simple finite element method in vorticity formulation for incompressible flow, Math. Comp., vol. 69 (2001), pp. 1385-1407 .
  40. 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 .
  41. Weinan E and J.-G. Liu, Gauge finite element method for incompressible flows, Int. J. Num. Meth. Fluids, vol. 34 (2000), pp. 701-710 .
  42. C. Wang and J.-G. Liu, Convergence of gauge method for incompressible flow, Math. Comp., vol. 69 (2000), pp. 1385-1407 .
  43. 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 .
  44. 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 .
Papers Accepted
  1. Y.-L. Huang, J.-G. Liu and W.-C. Wang, An FFT based fast Poisson solver on spherical shells, Commun. Comput. Phy. (2009) .
  2. J.-G. Liu and R. Pego, Stable discretization of magnetohydrodynamics in bounded domains, Commun. Math. Sci. (2009) .