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.