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Low regularity solutions to the logarithmic Schrödinger equation

Rémi Carles, Masayuki Hayashi and Tohru Ozawa
Vol. 6 (2024), No. 3, 859–871
DOI: 10.2140/paa.2024.6.859
Abstract

We consider the logarithmic Schrödinger equation, in various geometric settings. We show that the flow map can be uniquely extended from H1 to L2, and that this extension is Lipschitz continuous. Moreover, we prove the regularity of the flow map in intermediate Sobolev spaces.

Keywords
nonlinear Schrödinger equation, logarithmic nonlinearity, low regularity
Mathematical Subject Classification
Primary: 35B30, 35Q55
Secondary: 35B65
Milestones
Received: 3 November 2023
Revised: 8 January 2024
Accepted: 18 March 2024
Published: 1 October 2024
Authors
Rémi Carles
Université de Rennes, CNRS
IRMAR, UMR 6625
Rennes
France
Masayuki Hayashi
Dipartimento di Matematica
Università di Pisa
Pisa
Italy		 Waseda Research Institute for Science and Engineering
Waseda University
Tokyo
Japan
Tohru Ozawa
Department of Applied Physics
Waseda University
Tokyo
Japan
© 2024 MSP (Mathematical Sciences Publishers).