Global well--posedness for the mass--critical nonlinear Schr{ö}dinger equation on $\mathbb{T}$

Benjamin Dodson

Global well--posedness for the mass--critical nonlinear Schr{ö}dinger equation on $\mathbb{T}$

Analysis of PDEs 2026-07-02 v1

Authors: Benjamin Dodson

Abstract

We prove a global well--posedness result for the quintic NLS on $\mathbb{T}$ for initial data in $H^{s}(\mathbb{T})$ , $s > 1/3$ . This improves the previous best bound of $s > 2/5$ .

Keywords

global well-posedness mass-critical NLS quintic NLS torus Sobolev spaces

Cite

@article{arxiv.2607.02257,
  title  = {Global well--posedness for the mass--critical nonlinear Schr{ö}dinger equation on $\mathbb{T}$},
  author = {Benjamin Dodson},
  journal= {arXiv preprint arXiv:2607.02257},
  year   = {2026}
}