Strong solutions of the coupled Navier-Stokes-Poisson equations for isentropic compressible fluids

Abstract

In this article, we are concerned with the strong solutions of the coupled Navier-Stokes-Poisson equations for isentropic compressible fluids in a domain Ω ⊂ R 3. We prove the local existence of unique strong solutions provided that the initial data ϱ 0 and u 0 satisfy a nature compatibility condition. The important point in this article is that we allow the initial vacuum: the initial density may vanish in an open subset of Ω. This is achieved by getting some uniform estimates and using a Schauder fixed point theorem.