Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system

Marion Acheritogaray; Pierre Degond; Amic Frouvelle; Jian-Guo Liu

doi:10.3934/krm.2011.4.901

Article Contents

2011, Volume 4, Issue 4: 901-918. Doi: 10.3934/krm.2011.4.901

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Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system

1.
1-Université de Toulouse; UPS, INSA, UT1, UTM, Institut de Mathmatiques de Toulouse, F-31062 Toulouse
2.
Department of Physics and Department of Mathematics, Duke University, Durham, NC 27708

Received: June 30, 2011

Revised: July 31, 2011

Published: November 2011

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Abstract

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 equations 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.

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Mathematics Subject Classification: Primary: 35L60; Secondary: 35K55, 35Q80.

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