On an inhomogeneous boundary value problem for steady compressible magnetohydrodynamics flow

Abstract

In this paper, we are concerned with the three-dimensional stationary equations of compressible magnetohydrodynamic (MHD) isentropic flow in a bounded cylinder domain $$\Omega =(0,1)\times \Omega _0$$ with an inhomogeneous boundary condition. We obtain the existence and uniqueness of a strong solution provided that the data are around a given constant flow. From our result, it reveals that the magnetic Reynolds number plays an important role in the stability of steady compressible MHD equations.