English

Low regularity solutions to the logarithmic Schrodinger equation

Analysis of PDEs 2025-07-23 v2

Abstract

We consider the logarithmic Schr{\"o}dinger equation, in various geometric settings. We show that the flow map can be uniquely extended from H^1 to L^2 , and that this extension is Lipschitz continuous. Moreover, we prove the regularity of the flow map in intermediate Sobolev spaces.

Keywords

Cite

@article{arxiv.2311.01801,
  title  = {Low regularity solutions to the logarithmic Schrodinger equation},
  author = {Rémi Carles and Masayuki Hayashi and Tohru Ozawa},
  journal= {arXiv preprint arXiv:2311.01801},
  year   = {2025}
}

Comments

Some typos fixed. A flaw corrected in Section 4

R2 v1 2026-06-28T13:10:28.985Z