Séminaire EDP-Analyse ICJ

Long time stability for cubic nonlinear Schrödinger equations on non-rectangular flat tori.

by Joackim Bernier (LMJL - Nantes Université)

Fokko (ICJ)




 I will present and discuss a result we recently proved with Nicolas Camps. We consider nonlinear Schrödinger equations on flat tori satisfying a simple and explicit Diophantine non-degeneracy condition. Provided that the nonlinearity contains a cubic term, we prove the almost global existence and stability of most of the small solutions in high regularity Sobolev spaces.