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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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