Time periodic solution for a 3-D compressible Navier–Stokes system with an external force in R3R3

This paper is concerned with the existence of time periodic solutions of a compressible Navier–Stokes system in the whole space R3R3 with u→0u→0, ρ→ρ¯ as |x|→∞|x|→∞. We first solve the problem in a sequence of bounded domains, and letting the sequence tend to the original unbounded domain R3R3, we obtain the existence of a strong small periodic solution as the limit of the corresponding sequence of solutions in the bounded domains.