Research Interests for Jian-Guo Liu

Research Interests: Numerical Analysis, Partial Differential Equations, Computational Fluid Dynamics

Areas of Interest:

Numerical Analysis
Partial Differential Equations
Computational Fluid Dynamics

Representative Publications
  1. 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. (Accepted, 2011)
  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, Jie Liu and R. Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow, J. Comput. Phys., vol. 229 (2010), pp. 3428-3453
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. Weinan E and J.-G. Liu, Gauge method for viscous incompressible flows, Comm. Math. Sci., vol. 1 (2003), pp. 317--332
  10. Weinan E and J.-G. Liu, Essential compact scheme for unsteady viscous incompressible flows, J. Comput. Phys., vol. 126 (1996), pp. 122-138
  11. 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
  12. 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
  13. 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