Nonlinear instability in an ideal fluid. (English) Zbl 0874.76026

Summary: Linearized instability implies nonlinear instability under certain rather general conditions. This abstract theorem is applied to the Euler equations governing the motion of an inviscid fluid. In particular, this theorem can be applied to all two-dimensional space periodic flows without stagnation points as well as to two-dimensional space-periodic shear flows.


76E30 Nonlinear effects in hydrodynamic stability
76B47 Vortex flows for incompressible inviscid fluids
35Q35 PDEs in connection with fluid mechanics
Full Text: DOI Numdam EuDML


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