On the global existence and time decay estimates in critical spaces for the Navier-Stokes-Poisson system

We are concerned with the study of the Cauchy problem for the Navier-Stokes-Poisson system in the critical regularity framework. In the case of a repulsive potential, we first establish the unique global solvability in any dimension n >= 2 for small perturbations of a linearly stable constant state. Next, under a suitable additional condition involving only the low frequencies of the data and in the L-2-critical framework (for simplicity), we exhibit optimal decay estimates for the constructed global solutions, which are similar to those of the barotropic compressible Navier-Stokes system. Our results rely on new a priori estimates for the linearized Navier-Stokes-Poisson system about a stable constant equilibrium, and on a refined time-weighted energy functional. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim