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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
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