Energy Critical NLS in two space dimensions
Analysis of PDEs
2008-06-19 v1
Abstract
We investigate the initial value problem for a defocusing nonlinear Schr\"odingerequation with exponential nonlinearity. We identify subcritical, critical and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.
Keywords
Cite
@article{arxiv.0806.2979,
title = {Energy Critical NLS in two space dimensions},
author = {Jim Colliander and Slim Ibrahim and Mohamed Majdoub and Nader Masmoudi},
journal= {arXiv preprint arXiv:0806.2979},
year = {2008}
}
Comments
27 pages, submitted