JournalsaihpcVol. 31, No. 3pp. 555–565

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
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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