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Pré-Publication, Document De Travail Année : 2007

Sequential loss of regularity for super-critical nonlinear Schrodinger equations

Thomas Alazard
Rémi Carles

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, namely that 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.
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Dates et versions

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

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Thomas Alazard, Rémi Carles. Sequential loss of regularity for super-critical nonlinear Schrodinger equations. 2007. ⟨hal-00127815v1⟩
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