Counter-examples to concentration-cancellation and supercritical nonlinear geometric optics for the incompressible Euler equations

Abstract. We study the existence and the asymptotic behavior of large ampli-tude high-frequency oscillating waves subjected to the 2D Burger equation. This program is achieved by developing tools related to supercritical WKB analysis. By selecting solutions which are divergence free, we show that incompressible or compressible 2D Euler equations are not locally closed for the weak L2 topology. 1 Introduction. This article is devoted to the study of the two dimensional incompressible Euler equation (1.1) ∂tu + (u · ∇x)u+∇xp = 0, divx u = 0 as well as to the study of the two dimensional Burger equatio