On the nonlinear instability of Euler and Prandtl equations

In this paper we give examples of nonlinearly unstable solutions of Euler equations in the whole space ℝ2, the half space ℝ × ℝ+, the periodic strip ℝ × 𝕋, the strip ℝ × [−1,1], and the periodic torus 𝕋2, with an application to vortex sheets. Using the same methods, we prove an instability result for Prandtl-type boundary layers that appear in ℝ × ℝ+ and 𝕋 × ℝ+.