等熵可压Navier-Stokes-Poisson方程局部强解适定性

数学物理学报 ›› 2009, Vol. 29 ›› Issue (4): 985-1000.

等熵可压Navier-Stokes-Poisson方程局部强解适定性

(厦门大学数学科学学院, 福建厦门 361005, 北京应用物理与计算数学所, 北京 100088)

收稿日期:2007-01-28 修回日期:2008-03-15 出版日期:2009-08-25 发布日期:2009-08-25
基金资助:
国家自然科学基金(10531020)、厦门大学新世纪优秀人才资助计划(NCETXMU)资助

Local Strong Solutions of Navier-Stokes-Poisson Equations for Isentropic Compressible Fluids

(School of Mathematics, Xiamen University, Fujian |Xiamen 361005, Institute of Applied Physics and Computational Mathematics, Beijing 100088)

Received:2007-01-28 Revised:2008-03-15 Online:2009-08-25 Published:2009-08-25
Supported by:
国家自然科学基金(10531020)、厦门大学新世纪优秀人才资助计划(NCETXMU)资助

摘要/Abstract

摘要：

该文得到了三维情形等熵可压Navier-Stokes-Poisson方程局部强解的存在性、唯一性及稳定性. 重要的是,该文允许初始密度真空的存在. 首先用推广形式的Gronwall不等式得到了强解的局部存在性,然后得到了较弱条件下的唯一性,在证明唯一性的同时得到了稳定性.

关键词: 局部强解, Navier-Stokes-Poisson方程, 存在性, 唯一性, 稳定性

Abstract:

In this paper, the authors prove the existence, uniqueness, stability of the local strong solutions for Navier-Stokes-Poisson equations in three dimensions. The important point is that they allow the initial vacuum: the initial density may vanish in a boundary and open subset. The local existence is gotten by the extended Gronwall's inequality, then the authors prove the uniqueness in weaker condition. Finally, from the proof of the uniquenss, the stability can be concluded naturally.

Key words: Local strong solutions, Navier-Stokes-Poisson equations, Existence, Uniqueness, Stability

中图分类号:

35A05

尹俊平, 谭忠. 等熵可压Navier-Stokes-Poisson方程局部强解适定性[J]. 数学物理学报, 2009, 29(4): 985-1000.

YIN Jun-Peng, TAN Zhong. Local Strong Solutions of Navier-Stokes-Poisson Equations for Isentropic Compressible Fluids[J]. Acta mathematica scientia,Series A, 2009, 29(4): 985-1000.

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