Scattering for the critical 2-D NLS with exponential growth

Hajer Bahouri; Slim Ibrahim; Galina Perelman

Scattering for the critical 2-D NLS with exponential growth

Analysis of PDEs 2013-02-07 v1

Authors: Hajer Bahouri , Slim Ibrahim , Galina Perelman

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.

Keywords

nonlinear schrödinger equation scattering theory schrödinger equation

Cite

@article{arxiv.1302.1269,
  title  = {Scattering for the critical 2-D NLS with exponential growth},
  author = {Hajer Bahouri and Slim Ibrahim and Galina Perelman},
  journal= {arXiv preprint arXiv:1302.1269},
  year   = {2013}
}

Related papers

View all related →