Global well-posedness of strong solutions to the magnetohydrodynamic equations of compressible flows

This paper is concerned with the global well-posedness of strong solutions to the compressible MHD equations in a bounded domain Ω⊂R3Ω⊂R3. We first establish the local existence and uniqueness of strong solutions with arbitrary initial data and external force field. Based on the local existence result and some a priori estimates, the global existence and large time behavior of strong solutions are proved, under the assumptions that the initial data and external force field are small enough. Furthermore, the existence of the time periodic solution is also obtained when the external force field is time periodic.