Remarks on the nonlinear instability of incompressible Euler equations |
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Authors: | Xie Huazhao Zi Ruizhao |
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Institution: | aDepartment of Mathematics, Henan University of Economics and Law, Zhengzhou 450002, China;bDepartment of Mathematics, Zhejiang University, Hangzhou 310027, China |
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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 nonlinear 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. |
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Keywords: | Euler equations incompressible nonlinear instability |
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