English

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