Loss of regularity for supercritical nonlinear Schrodinger equations - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Article Dans Une Revue Mathematische Annalen Année : 2009

Loss of regularity for supercritical nonlinear Schrodinger equations

Résumé

We consider the nonlinear Schrodinger equation with defocusing, smooth, nonlinearity. Below the critical Sobolev regularity, it is known that the Cauchy problem is ill-posed. We show that this is even worse: there is a loss of regularity, in the same spirit as the result due to G.Lebeau in the case of the wave equation. We use an isotropic change of variable, which reduces the problem to a super-critical WKB analysis. For super-cubic, smooth nonlinearity, this analysis is new, and relies on the introduction of a modulated energy functional a la Brenier.
Fichier principal
Vignette du fichier
lost.pdf (288.22 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00127815 , version 1 (29-01-2007)
hal-00127815 , version 2 (13-07-2007)
hal-00127815 , version 3 (25-02-2008)

Identifiants

Citer

Thomas Alazard, Rémi Carles. Loss of regularity for supercritical nonlinear Schrodinger equations. Mathematische Annalen, 2009, 343 (2), pp.397-420. ⟨10.1007/s00208-008-0276-6⟩. ⟨hal-00127815v3⟩
170 Consultations
363 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More