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.
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