Low regularity solutions to the logarithmic Schrodinger equation

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.

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Authors: Carles, Rémi, Hayashi, Masayuki, Ozawa, Tohru
Format: Article
Language:English
Subjects:
Flow mapping
Logarithms
Regularity
Schrodinger equation
Sobolev space
Online Access:Get full text
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Description
Summary: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.
ISSN:2331-8422