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Pré-Publication, Document De Travail Année : 2013

Scattering for the critical 2-D NLS with exponential growth

Résumé

In this article, we establish in the radial framework the $H^1$-scattering for the critical 2-D nonlinear Schrödinger equation with exponential growth. Our strategy relies on both the a priori estimate derived in \cite{CGT, PV} and the characterization of the lack of compactness of the Sobolev embedding of $H_{rad}^1(\R^2)$ into the critical Orlicz space ${\cL}(\R^2)$ settled in \cite{BMM}. The radial setting, and particularly the fact that we deal with bounded functions far away from the origin, occurs in a crucial way in our approach.

Dates et versions

hal-00796200 , version 1 (01-03-2013)

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Hajer Bahouri, Slim Ibrahim, Galina Perelman. Scattering for the critical 2-D NLS with exponential growth. 2013. ⟨hal-00796200⟩
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