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arXiv · 1302.1269

Scattering for the critical 2-D NLS with exponential growth

Hajer Bahouri·Slim Ibrahim·Galina Perelman
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Abstract

In this article, we establish in the radial framework the $H^1$-scattering for the critical 2-D nonlinear Schr\"odinger 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.

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Hajer Bahouri, Slim Ibrahim, Galina Perelman. 2013-02-06. Scattering for the critical 2-D NLS with exponential growth. https://arxiv.org/abs/1302.1269

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