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

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

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1280-1290.doi: 10.1016/S0252-9602(10)60124-5

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

谭忠¹, 张映辉^1,2*

1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
2. Department of Mathematics, Hunan Institute of Science and Technology, Yueyang |414006, China

收稿日期:2007-12-16 修回日期:2008-09-27 出版日期:2010-07-20 发布日期:2010-07-20
通讯作者: 张映辉 E-mail:ztan85@163.com; zhangyinghui1009@yahoo.com.cn
基金资助:
Supported by National Natural Science Foundation of China-NSAF (10976026)

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

TAN Zhong¹, ZHANG Ying-Hui^1,2*

1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China;
2. Department of Mathematics, Hunan Institute of Science and Technology, Yueyang |414006, China

Received:2007-12-16 Revised:2008-09-27 Online:2010-07-20 Published:2010-07-20
Contact: ZHANG Ying-Hui E-mail:ztan85@163.com; zhangyinghui1009@yahoo.com.cn
Supported by:
Supported by National Natural Science Foundation of China-NSAF (10976026)

摘要/Abstract

摘要：

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.

关键词: Strong solutions, Navier-Stokes-Poisson equations, Schauder fixed point theorem

Abstract:

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

中图分类号:

35L65

谭忠, 张映辉. STRONG SOLUTIONS OF THE COUPLED NAVIER-STOKES-POISSON EQUATIONS FOR ISENTROPIC COMPRESSIBLE FLUIDS[J]. 数学物理学报(英文版), 2010, 30(4): 1280-1290.

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

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

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