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arXiv · 2308.12758

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

Chenmin Sun·Nikolay Tzvetkov
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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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Chenmin Sun, Nikolay Tzvetkov. 2023-08-24. Quasi-invariance of Gaussian measures for the $3d$ energy critical nonlinear Schr\" odinger equation. https://arxiv.org/abs/2308.12758

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