Long Time Behavior of Weak Solutions to Navier–Stokes–Poisson System

Abstract

Ducomet et al. (Discrete Contin Dyn Syst 11(1): 113–130, 2004) showed the existence of global weak solutions to the Navier–Stokes–Poisson system. We study the global behavior of such a solution. This is done by (1) proving uniqueness of a solution to the stationary system; (2) by showing convergence of a weak solution to the stationary solution. In (1) we consider only the case with repulsion. We prove our result in the case of a bounded domain with smooth boundary in \({\mathbb{R}^3}\) and also in the case of the whole space \({\mathbb{R}^3}\).