On the nonlinear instability of Euler and Prandtl equations

In this paper we give examples of nonlinearly unstable solutions of Euler e quations in the whole space R-2, the half space R x R+, the periodic strip R x T, the strip R x [-1, 1], and the periodic torus T-2, with an applicati on to vortex sheets. Using the same methods, we prove an instability result for Prandtl-type boundary layers that appear in R x R+ and T x R+. (C) 200 0 John Wiley & Sons, Inc.