On 2D NLS on non-trapping exterior domains
Analysis of PDEs
2013-12-06 v2
Abstract
Global existence and scattering for the nonlinear defocusing Schr\"odinger equation in 2 dimensions are known for domains exterior to star-shaped obstacles and for nonlinearities that grow at least as the quintic power. In this paper, we extend the global existence result for all non-trapping obstacles and for nonlinearities with power strictly greater than quartic. For such nonlinearities, we also prove scattering for a class of so-called almost star-shaped obstacles.
Keywords
Cite
@article{arxiv.1304.7628,
title = {On 2D NLS on non-trapping exterior domains},
author = {Farah Abou Shakra},
journal= {arXiv preprint arXiv:1304.7628},
year = {2013}
}
Comments
fixed typos and updated references, to appear in Revista Matem\'atica Iberoamericana