Counter-Examples to the Concentration-Cancellation Property

Christophe Cheverry (1) , Olivier Guès (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We study the existence and the asymptotic behavior of large amplitude 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 $ L^2 $ topology.

Mots clés: supercritical analysis; nonlinear geometric optics; Euler equations

Domaines: Equations aux dérivées partielles [math.AP]

Christophe Cheverry, Olivier Guès. Counter-Examples to the Concentration-Cancellation Property. Archive for Rational Mechanics and Analysis, 2008, 189 (3), pp.363-424. ⟨hal-00005057v2⟩