Quasi-invariance of Gaussian measures for the $3d$ energy critical nonlinear Schr\" odinger equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916725206810624 |
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| author | Sun, Chenmin Tzvetkov, Nikolay |
| author_facet | Sun, Chenmin Tzvetkov, Nikolay |
| contents | We consider the $3d$ energy critical nonlinear Schr\" odinger equation with data distributed according to the Gaussian measure with covariance operator $(1-Δ)^{-s}$, where $Δ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12758 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quasi-invariance of Gaussian measures for the $3d$ energy critical nonlinear Schr\" odinger equation Sun, Chenmin Tzvetkov, Nikolay Analysis of PDEs Probability We consider the $3d$ energy critical nonlinear Schr\" odinger equation with data distributed according to the Gaussian measure with covariance operator $(1-Δ)^{-s}$, where $Δ$ 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. |
| title | Quasi-invariance of Gaussian measures for the $3d$ energy critical nonlinear Schr\" odinger equation |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2308.12758 |