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

Abstract

This paper deals with the model of compressible viscous and barotropic fluids coupled with the Poisson equation in a bounded domain Ω⊂R3 with C2+α (0 < α < 1) boundary ∂Ω. We prove the existence and weak-strong uniqueness of dissipative solutions when the adiabatic exponent γ > 1. We find that the Poisson term ρ∇Φ is not integrable when γ∈(1,32). We will make full use of the Poisson equation and energy inequality to overcome this difficulty. Finally, we obtain that ρ∇Φ leads to the decrease of Reynolds stress R and the increase of the energy dissipation defect E.