Global stability of steady supersonic compressible MHD flow with friction in a straight duct

In this paper we will consider the global stability of steady compressible supersonic magnetohydrodynamic ow with friction in one-dimensional straight duct. Given a steady supersonic ow at the duct entrance, we determine the maximum duct length to maintain supersonic ow throughout the duct and establish the global existence of steady solution. Furthermore, using wave decomposition, we will establish the global stability of the steady ow for the unsteady MHD system under small perturbations of initial-boundary conditions.