# American Institute of Mathematical Sciences

December  2012, 5(4): 743-767. doi: 10.3934/krm.2012.5.743

## Global existence in critical spaces for the compressible magnetohydrodynamic equations

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

Received  January 2012 Revised  March 2012 Published  November 2012

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.
Citation: Qing Chen, Zhong Tan. Global existence in critical spaces for the compressible magnetohydrodynamic equations. Kinetic & Related Models, 2012, 5 (4) : 743-767. doi: 10.3934/krm.2012.5.743
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