Acta mathematica scientia, Series B >
REMARKS ON THE NONLINEAR INSTABILITY OF INCOMPRESSIBLE EULER EQUATIONS
Received date: 2010-01-21
Online 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).
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
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 . DOI: 10.1016/S0252-9602(11)60367-6
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