Time periodic solution to the compressible Euler equations with damping in a periodic domain

Abstract

In this paper, we consider the existence and uniqueness of a time periodic solution to the three-dimensional compressible damped Euler equations in a periodic domain. By adapting a regularized approximation scheme and applying the topological degree theory, we establish the existence of the time periodic solution under some smallness and structure assumptions imposed on a time periodic force. And based on energy estimates, the uniqueness of the periodic solution is proved.