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Nonlinear instability in two-dimensional ideal fluids: the case of a dominant eigenvalue. (English) Zbl 1043.76025
Summary: It is proved that any steady two-dimensional ideal fluid flow is nonlinearly unstable with respect to $$L^2$$ growth in the velocity, provided there exists an eigenvalue $$\lambda$$ for the linearised Euler equation with Re$$\lambda>\Lambda$$. Here $$\Lambda$$ is the maximal Lyapunov exponent of the steady flow.

##### MSC:
 76E30 Nonlinear effects in hydrodynamic stability 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids 35Q35 PDEs in connection with fluid mechanics
##### Keywords:
linearized Euler equation; maximal Lyapunov exponent
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