Optimal convergence rates for the strong solutions to the compressible Navier-Stokes equations with potential force

In this paper, we consider the effect of external force on the large-time behavior of solutions to the Cauchy problem for the three-dimensional full compressible Navier-Stokes equations. We construct the global unique solution near the stationary profile to the system for the small H2(R3) initial data. Moreover, the optimal Lp-L2(1≤p≤2) time decay rates of the solution to the system are established via a low frequency and high frequency decomposition.