Global weak solutions to 3D compressible Navier-Stokes-Poisson equations with density-dependent viscosity

In this paper, we study the global existence of weak solutions to the compressible Navier-Stokes-Poisson (N-S-P) equations with density-dependent viscosity and non-monotone pressure in a three dimensional torus. Our approach is based on the Faedo-Galerkin method and the compactness arguments. Motivated by Vasseur-Yu [29] and [30], we construct the approximate solutions and the key estimates ling in the elementary energy estimates, B-D entropy and Mellet-Vasseur type inequality for the weak solutions. Here, we need the conditions that the adiabatic constant γ satisfies 43<γ<3, for λ=−1 or 1<γ<3, for λ=1, where λ is a sign constant of Poisson equation which determines the physical meaning of the N-S-P system.