Kinetic formulation and global existence for the hall-magneto-hydrodynamics system


Journal Article

This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits. We also propose a kinetic formulation for the Hall-MHD equa- tions which contains as fluid closure different variants of the Hall-MHD model. Then, we prove the existence of global weak solutions for the incompressible viscous resistive Hall-MHD model. We use the particular structure of the Hall term which has zero contribution to the energy identity. Finally, we discuss particular solutions in the form of axisymmetric purely swirling magnetic fields and propose some regularization of the Hall equation. © American Institute of Mathematical Sciences.

Full Text

Duke Authors

Cited Authors

  • Acheritogaray, M; Degond, P; Frouvelle, A; Liu, JG

Published Date

  • December 1, 2011

Published In

Volume / Issue

  • 4 / 4

Start / End Page

  • 901 - 918

Electronic International Standard Serial Number (EISSN)

  • 1937-5077

International Standard Serial Number (ISSN)

  • 1937-5093

Digital Object Identifier (DOI)

  • 10.3934/krm.2011.4.901

Citation Source

  • Scopus