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Low
regularity solutions to the logarithmic Schrödinger
equation
Rémi Carles, Masayuki Hayashi and Tohru Ozawa |
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Vol. 6 (2024), No. 3, 859–871
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Abstract |
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We consider the logarithmic Schrödinger equation, in various geometric settings. We show that the flow map can be uniquely extended from to , and that this extension is Lipschitz continuous. Moreover, we prove the regularity of the flow map in intermediate Sobolev spaces. |
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Keywords
nonlinear Schrödinger equation, logarithmic nonlinearity,
low regularity
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Mathematical Subject Classification
Primary: 35B30, 35Q55
Secondary: 35B65
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Milestones
Received: 3 November 2023
Revised: 8 January 2024
Accepted: 18 March 2024
Published: 1 October 2024
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Authors |
| Rémi Carles | |
| Université de Rennes, CNRS IRMAR, UMR 6625 Rennes France |
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| 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 |
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| © 2024 MSP (Mathematical Sciences Publishers). |
