Abstract
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 [10, 23] and the characterization of the lack of compactness of the Sobolev embedding of $H_{rad}^1(\mathbb R^2)$ into the critical Orlicz space ${\mathcal L}(\mathbb R^2)$ settled in [4]. 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.
Citation
Hajer Bahouri. Slim Ibrahim. Galina Perelman. "Scattering for the critical 2-D NLS with exponential growth." Differential Integral Equations 27 (3/4) 233 - 268, March/April 2014. https://doi.org/10.57262/die/1391091365
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