The defocusing quintic NLS in four space dimensions
Analysis of PDEs
2017-07-18 v1
Abstract
We consider the defocusing quintic nonlinear Schr\"odinger equation in four space dimensions. We prove that any solution that remains bounded in the critical Sobolev space must be global and scatter. We employ a space-localized interaction Morawetz inequality, the proof of which requires us to overcome the logarithmic failure in the double Duhamel argument in four dimensions.
Cite
@article{arxiv.1508.07298,
title = {The defocusing quintic NLS in four space dimensions},
author = {Benjamin Dodson and Changxing Miao and Jason Murphy and Jiqiang Zheng},
journal= {arXiv preprint arXiv:1508.07298},
year = {2017}
}
Comments
29 pages