# American Institute of Mathematical Sciences

December  2017, 10(4): 1235-1253. doi: 10.3934/krm.2017047

## The stability of contact discontinuity for compressible planar magnetohydrodynamics

 School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

* Corresponding author: Haiyan Yin

Received  October 2016 Revised  January 2017 Published  March 2017

This paper is concerned with the planar magnetohydrodynamicswith initial data whose behaviors at far fields $x\rightarrow \pm\infty$ are different. Motivated by the relationship between planar magnetohydrodynamics and Navier-Stokes, we can prove that the solutions to the planar magnetohydrodynamics tend time-asymptotically to a viscous contact wave which is constructed from a contact discontinuity solution of the Riemann problemon Euler system. This result is proved by the method of elementary energy estimates.

Citation: Haiyan Yin. The stability of contact discontinuity for compressible planar magnetohydrodynamics. Kinetic & Related Models, 2017, 10 (4) : 1235-1253. doi: 10.3934/krm.2017047
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