Existence and stability of stationary solutions to the compressible Navier–Stokes–Poisson equations

In this paper, we are concerned with the compressible Navier–Stokes–Poisson equations with the given external force of general form in three dimensional space. Based on the weighted L2L2 method and the contraction mapping principle, we prove the existence and uniqueness of stationary solutions. Then, we show the stability of solutions to the Cauchy problem near the stationary state provided that the initial perturbation is sufficiently small. Finally, the time decay rates of the solutions are obtained when the initial perturbation belongs to Ḣ−s with 0≤s<32.