Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (5): 1877-1888.doi: 10.1016/S0252-9602(11)60367-6

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REMARKS ON THE NONLINEAR INSTABILITY OF INCOMPRESSIBLE EULER EQUATIONS

 XIE Hua-Chao, ZI Rui-Zhao   

  1. 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).

Abstract:

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.

Key words: Euler equations, incompressible, nonlinear instability

CLC Number: 

  • 35Q05
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