Scattering for the critical 2-D NLS with exponential growth
2014; Khayyam Publishing; Volume: 27; Issue: 3/4 Linguagem: Inglês
10.57262/die/1391091365
ISSN0893-4983
AutoresHajer Bahouri, Slim Ibrahim, Galina Perelman,
Tópico(s)Nonlinear Partial Differential Equations
ResumoIn 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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