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In this article, we establish in the radial framework the $H^1$-scatteringfor 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} andthe 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 withbounded functions far away from the origin, occurs in a crucial way in ourapproach.

Scattering for the critical 2-D NLS with exponential growth