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

Abstract 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 4 3 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.