Generalized solutions to the model of compressible viscous fluids coupled with the Poisson equation

This paper deals with the model of compressible viscous and barotropic fluids coupled with the Poisson equation in a bounded domain Omega subset of R-3 with C2+alpha (0 < alpha < 1) boundary partial derivative Omega. We prove the existence and weak-strong uniqueness of dissipative solutions when the adiabatic exponent gamma > 1. We find that the Poisson term rho del Phi is not integrable when gamma is an element of (1, 3/2). We will make full use of the Poisson equation and energy inequality to overcome this difficulty. Finally, we obtain that rho del Phi leads to the decrease of Reynolds stress R and the increase of the energy dissipation defect E.