Asymptotic stability of viscous shock profiles for compressible planar magnetohydrodynamics system

This paper shows time-asymptotic nonlinear stability and existence of the viscous shock profiles to the Cauchy problem of the one-dimensional compressible planar magnetohydrodynamics system, which describes the motions of a conducting fluid in an electro-magnetohydrodynamics system. We can prove that the solutions to the compressible planar magnetohydrodynamics system tend time-asymptotically to the viscous shock profiles provided that the initial disturbance is small and of integral zero.