Quasi‐invariance of Gaussian measures for the 3d$3d$ energy critical nonlinear Schrödinger equation

We consider the energy critical nonlinear Schrödinger equation with data distributed according to the Gaussian measure with covariance operator , where is the Laplace operator and is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple...

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Bibliographic Details
Published inCommunications on pure and applied mathematics
Main Authors Sun, Chenmin, Tzvetkov, Nikolay
Format Journal Article
LanguageEnglish
Published 26.06.2025
Online AccessGet full text
ISSN0010-3640
1097-0312
DOI10.1002/cpa.70001

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Summary:We consider the energy critical nonlinear Schrödinger equation with data distributed according to the Gaussian measure with covariance operator , where is the Laplace operator and is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple applications. This extends a previous result by Planchon‐Visciglia and the second author from to higher dimensions.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.70001