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 ̇ − 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.