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

• 论文 • 上一篇    下一篇

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

谭忠1, 张映辉1,2*   

  1. 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-Hui1,2*   

  1. 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:

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 u0 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.

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

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 u0 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.

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

中图分类号: 

  • 35L65