Global well-posedness for the cubic fractional NLS on the unit disk
Analysis of PDEs
2022-03-28 v2
Abstract
In this paper, we prove that the cubic nonlinear Schr\"odinger equation with the fractional Laplacian on the unit disk is globally well-posed for certain radial initial data below the energy space. The result is proved by extending the I-method in the fractional nonlinear Schr\"odinger equation setting.
Keywords
Cite
@article{arxiv.2011.05517,
title = {Global well-posedness for the cubic fractional NLS on the unit disk},
author = {Mouhamadou Sy and Xueying Yu},
journal= {arXiv preprint arXiv:2011.05517},
year = {2022}
}
Comments
Detailed proof of claim 5.5 added