Stability of stationary solution for the compressible viscous magnetohydrodynamic equations with large potential force in bounded domain

Abstract

In this paper, we consider the 3-D compressible viscous magnetohydrodynamic (MHD) equations with some large potential force in bounded rigid vessel. We firstly construct the non-constant stationary solutions of the compressible viscous MHD equations under suitable constitutive assumptions. Next, a critical energy identity is established to achieve a universal stability criterion of the stationary solution. In this case, the stationary solution is exponential stable for any large external potential force. Finally, we show the well-posedness of the initial boundary value problem for the compressible viscous MHD equations with the large potential force, provided that the prescribed initial data is close to the stationary solution. It implies that the set satisfying the stability criterion is not empty.