Optimal decay rate for the compressible Navier-Stokes-Poisson system in the critical Lp framework

In this paper, we consider the large time behavior of global solutions to the initial value problem for the compressible Navier-Stokes-Poisson system in the Lp critical framework and in any dimension N≥3. We obtain the time decay rates, not only for Lebesgue spaces, but also for a family of Besov norms with negative or nonnegative regularity exponents, which improves the decay results in high Sobolev regularity. The proof is mainly based on the Littlewood-Paley theory and refined time weighted inequalities in Fourier space.