Global existence in critical spaces for the compressible magnetohydrodynamic equations

Qing Chen; Zhong Tan

doi:10.3934/krm.2012.5.743

Article Contents

2012, Volume 5, Issue 4: 743-767. Doi: 10.3934/krm.2012.5.743

This issue Previous Article Time evolution of a Vlasov-Poisson plasma with magnetic confinement Next Article On the gain of regularity for the positive part of Boltzmann collision operator associated with soft-potentials

Global existence in critical spaces for the compressible magnetohydrodynamic equations

Qing Chen^1, and
Zhong Tan^2,

1.
Department of Mathematics and Physics, Xiamen University of Technology, Xiamen, Fujian 361024
2.
School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005

Received: December 31, 2011

Revised: February 29, 2012

Published: November 2012

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Abstract

In this paper, we are concerned with the global existence and uniqueness of the strong solutions to the compressible Magnetohydrodynamic equations in $\mathbb{R}^N(N\ge3)$. Under the condition that the initial data are close to an equilibrium state with constant density, temperature and magnetic field, we prove the global existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations.

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Mathematics Subject Classification: Primary: 35Q35, 35D35; Secondary: 76N10.

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