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Quasi-invariance of Gaussian measures for the $3d$ energy critical nonlinear Schr\" odinger equation

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arxiv 2308.12758 v3 pith:UHP4XP3M submitted 2023-08-24 math.AP math.PR

Chenmin Sun , Nikolay Tzvetkov This is my paper · ORCID
classification math.APmath.PR
keywords measurecriticaldeltaenergyequationfullgaussiannonlinear
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abstract

We consider the $3d$ energy critical nonlinear Schr\" odinger equation with data distributed according to the Gaussian measure with covariance operator $(1-\Delta)^{-s}$, where $\Delta$ is the Laplace operator and $s$ 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 $1d$ to higher dimensions.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. New invariant surface measures for the cubic Schr\"odinger equation

    math.AP 2025-02 conditional novelty 6.0 of 10

    The authors construct invariant probability measures supported on level sets of the renormalized mass for the defocusing cubic nonlinear Schrodinger equation on the one- and two-dimensional torus.

  2. Improved quasi-invariance result for the periodic Benjamin-Ono-BBM equation

    math.AP 2025-01 accept novelty 6.0 of 10

    Quasi-invariance of Gaussian measures under the BO-BBM flow is established for the full global well-posedness range s > 1/2, improving the previous threshold s > 1.

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