REMARKS ON THE NONLINEAR INSTABILITY OF INCOMPRESSIBLE EULER EQUATIONS

doi:10.1016/S0252-9602(11)60367-6

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1877-1888.doi: 10.1016/S0252-9602(11)60367-6

REMARKS ON THE NONLINEAR INSTABILITY OF INCOMPRESSIBLE EULER EQUATIONS

谢华朝|訾瑞昭

Department of Mathematics, Henan University of Economics and Law, Zhengzhou 450002, China|Department of Mathematics, Zhejiang University, Hangzhou 310027, China

收稿日期:2010-01-21 出版日期:2011-09-20 发布日期:2011-09-20
基金资助:
The research of Xie was supported by the NSFC (11071094). The research of Zi was supported by the NSFC (The Youth Foundation) (10901068) and CCNU Project (CCNU09A01004).

REMARKS ON THE NONLINEAR INSTABILITY OF INCOMPRESSIBLE EULER EQUATIONS

XIE Hua-Chao, ZI Rui-Zhao

Department of Mathematics, Henan University of Economics and Law, Zhengzhou 450002, China|Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received:2010-01-21 Online:2011-09-20 Published:2011-09-20
Supported by:
The research of Xie was supported by the NSFC (11071094). The research of Zi was supported by the NSFC (The Youth Foundation) (10901068) and CCNU Project (CCNU09A01004).

摘要/Abstract

摘要：

In this paper, we consider the nonlinear instability of incompressible Euler equations. If a steady density is non-monotonic, then the smooth steady state is a non-linear instability. First, we use variational method to find a dominant eigenvalue which is important in the construction of approximate solutions, then by energy technique and analytic method, we obtain the dynamical instability result.

关键词: Euler equations, incompressible, nonlinear instability

Abstract:

Key words: Euler equations, incompressible, nonlinear instability

中图分类号:

35Q05

谢华朝, 訾瑞昭. REMARKS ON THE NONLINEAR INSTABILITY OF INCOMPRESSIBLE EULER EQUATIONS[J]. 数学物理学报(英文版), 2011, 31(5): 1877-1888.

XIE Hua-Chao, ZI Rui-Zhao. REMARKS ON THE NONLINEAR INSTABILITY OF INCOMPRESSIBLE EULER EQUATIONS[J]. Acta mathematica scientia,Series B, 2011, 31(5): 1877-1888.

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REMARKS ON THE NONLINEAR INSTABILITY OF INCOMPRESSIBLE EULER EQUATIONS

REMARKS ON THE NONLINEAR INSTABILITY OF INCOMPRESSIBLE EULER EQUATIONS

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