Vishik, Misha; Friedlander, Susan Nonlinear instability in two-dimensional ideal fluids: the case of a dominant eigenvalue. (English) Zbl 1043.76025 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. Cited in 19 Documents 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 PDF BibTeX XML Cite \textit{M. Vishik} and \textit{S. Friedlander}, Commun. Math. Phys. 243, No. 2, 261--273 (2003; Zbl 1043.76025) Full Text: DOI