Kinetic and Related Models (KRM)

The stability of contact discontinuity for compressible planar magnetohydrodynamics

Pages: 1235 - 1253, Volume 10, Issue 4, December 2017      doi:10.3934/krm.2017047

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Haiyan Yin - School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China (email)

Abstract: This paper is concerned with the planar magnetohydrodynamics with 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 problem on Euler system. This result is proved by the method of elementary energy estimates.

Keywords:  Planar magnetohydrodynamics, Riemann problem, contact discontinuity, large time behavior, stability.
Mathematics Subject Classification:  Primary: 76W05, 76D33; Secondary: 35B35.

Received: October 2016;      Revised: January 2017;      Available Online: March 2017.