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

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 conditi...

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Bibliographic Details
Published in:Acta mathematica scientia 2010-07, Vol.30 (4), p.1280-1290
Main Authors: Zhong, Tan, Yinghui, Zhang
Format: Article
Language:English
Subjects:
35L65
Navier-Stokes-Poisson equations
Schauder fixed point theorem
Strong solutions
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Summary: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.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(10)60124-5