Decay of the Navier–Stokes–Poisson equations

We establish the time decay rates of the solution to the Cauchy problem for the compressible Navier–Stokes–Poisson system via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. The (0⩽s<3/2) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. As a corollary, we also obtain the usual Lp–L2 (1