Global well-posedness of NLS with a rough potential below the energy norm
Analysis of PDEs
2013-01-04 v1
Abstract
We show that in the presence of a rough external potential, a 3d cubic defocusing NLS is globally well-posed in H^s for s>5/6. The proof is based on the approach of Colliander-Keel-Staffilani-Takaoka-Tao, called the I-method, but in order to deal with a rough potential, we modify harmonic analysis tools by spectral theory.
Keywords
Cite
@article{arxiv.1301.0428,
title = {Global well-posedness of NLS with a rough potential below the energy norm},
author = {Younghun Hong},
journal= {arXiv preprint arXiv:1301.0428},
year = {2013}
}