The radial defocusing nonlinear Schr\"odinger equation in three space dimensions
Analysis of PDEs
2015-01-16 v1
Abstract
We study the defocusing nonlinear Schr\"odinger equation in three space dimensions. We prove that any radial solution that remains bounded in the critical Sobolev space must be global and scatter. In the energy-supercritical setting, we employ a space-localized Lin--Strauss Morawetz inequality of Bourgain. In the inter-critical regime, we prove long-time Strichartz estimates and frequency-localized Lin--Strauss Morawetz inequalities.
Keywords
Cite
@article{arxiv.1401.4766,
title = {The radial defocusing nonlinear Schr\"odinger equation in three space dimensions},
author = {Jason Murphy},
journal= {arXiv preprint arXiv:1401.4766},
year = {2015}
}
Comments
37 pages