STRONG SOLUTIONS OF THE COUPLED NAVIER-STOKES-POISSON EQUATIONS FOR ISENTROPIC COMPRESSIBLE FLUIDS

doi:10.1016/S0252-9602(10)60124-5

Abstract

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 R³. We prove the local existence of unique strong solutions provided that the initial data ρ₀ and u₀satisfy 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.

Key words: Strong solutions, Navier-Stokes-Poisson equations, Schauder fixed point theorem

CLC Number:

35L65

TAN Zhong, ZHANG Ying-Hui. STRONG SOLUTIONS OF THE COUPLED NAVIER-STOKES-POISSON EQUATIONS FOR ISENTROPIC COMPRESSIBLE FLUIDS[J].Acta mathematica scientia,Series B, 2010, 30(4): 1280-1290.

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