数学物理学报 ›› 2016, Vol. 36 ›› Issue (2): 328-339.

• 论文 • 上一篇    下一篇

粘性非等熵流体方程平衡解的稳定性

谢华朝, 李素丽   

  1. 河南财经政法大学 数学与信息科学学院 郑州 450046
  • 收稿日期:2015-10-27 修回日期:2016-01-13 出版日期:2016-04-25 发布日期:2016-04-25
  • 作者简介:谢华朝,hzh_xie@126.com
  • 基金资助:

    国家自然科学基金(11326136,61203050)和河南省教育厅资助项目(14B110033,15A110010)资助

Stability for Stationary Solution of Non-Isentropic Viscous Fluid Equations

Xie Huazhao, Li Suli   

  1. Department of Mathematics, Henan University of Economics and Law, Zhengzhou 450046
  • Received:2015-10-27 Revised:2016-01-13 Online:2016-04-25 Published:2016-04-25
  • Supported by:

    Supported by the NSFC (11326136, 61203050) and the Fundamental Research Funds of Henan Province (14B110033, 15A110010)

摘要:

该文在三维空间中,研究Navier-Stokes-Poisson方程的平衡解及其非线性稳定性.当绝热指数4/3< γ< 2时,利用约束变分的方法得到N-S-P方程的平衡解,并且证明该平衡解是非线性稳定的.当γ=4/3时,证明在一定条件下平衡解是不稳定的.

关键词: Navier-Stokes-Poisson方程, 平衡解, 稳定性, 不稳定性

Abstract:

In three dimension space, we study the stationary solutions and nonlinear stability of Navier-Stokes-Poisson equations. Using variational method, we get the existence of stationary solution of N-S-P equations when 4/3< γ< 2, the nonlinear stability of such steady states is also proved. As γ=4/3, we prove the nonlinear instability of stationary solution.

Key words: Navier-Stokes-Poisson equations, Stationary solution, Stability, Instability

中图分类号: 

  • O175.2