Global existence and decay of strong solutions to the compressible Navier-Stokes-Poisson equations in bounded domains

Abstract

This paper concerns the global existence and decay rate of strong solutions to initial-boundary-value problem of the 3D compressible Navier-Stokes-Poisson equations. When the velocity admits slip boundary condition, it shows that strong solutions exist globally in time for small initial energy. The difficulties caused by Poisson term are overcome through uniform estimate of ‖ρ−1‖L2(0,T;L2) and time-weighted a priori estimates. In particular, the initial density has large oscillations and allows vacuum states. As a byproduct, we do not need any initial compatibility conditions.