English

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