Nonlinear instability in two-dimensional ideal fluids: the case of a dominant eigenvalue. (English) Zbl 1043.76025

Vishik, Misha; Friedlander, Susan

Commun. Math. Phys. 243, No. 2, 261-273 (2003).

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