Decay of the non-isentropic Navier-Stokes-Poisson equations

We establish the time decay rates of the solution to the Cauchy problem for the non-isentropic 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. As a corollary, we also obtain the usual L-P - L-2(1 < p <= 2) type of the optimal decay rates. The (H) over dot(-s)(0 <= s < 3/2) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. We use a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis. (C) 2012 Elsevier Inc. All rights reserved.