Periodic solutions to the compressible magnetohydrodynamic equations in a periodic domain

Abstract

In this paper, we study the compressible magnetohydrodynamic system with a time periodic external force in a periodic domain in Rn. Based on the idea in [12], we obtain the existence of a time periodic solution under some smallness and symmetry assumptions on the external force and improve the result from [12] in the following sense: we extend the space dimension from 3 to n, (n≥1). The uniqueness of the small periodic solution is also obtained.