Well-posedness for Hall-magnetohydrodynamics

  • Dongho Chae

    Department of Mathematics; Chung-Ang University, Seoul 156-756, Republic of Korea
  • Pierre Degond

    Université de Toulouse; UPS, INSA, UT1, UTM; Institut de Mathématiques de Toulouse; F-31062 Toulouse, France, CNRS; Institut de Mathématiques de Toulouse, UMR 5219; F-31062 Toulouse, France
  • Jian-Guo Liu

    Department of Physics and Department of Mathematics, Duke University, Durham, NC 27708, USA

Abstract

We prove local existence of smooth solutions for large data and global smooth solutions for small data to the incompressible, resistive, viscous or inviscid Hall-MHD model. We also show a Liouville theorem for the stationary solutions.

Cite this article

Dongho Chae, Pierre Degond, Jian-Guo Liu, Well-posedness for Hall-magnetohydrodynamics. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 3, pp. 555–565

DOI 10.1016/J.ANIHPC.2013.04.006