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

IF 2.7 1区数学 Q1 MATHEMATICS

Communications on Pure and Applied Mathematics Pub Date : 2025-06-26 DOI:10.1002/cpa.70001

Chenmin Sun, Nikolay Tzvetkov

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引用次数: 0

Abstract

We consider the $3 d$ energy critical nonlinear Schrödinger 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 $1 d$ to higher dimensions.

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三维$三维$能量临界非线性Schrödinger方程高斯测度的拟不变性

考虑数据按高斯测度分布的能量临界非线性Schrödinger方程，其中为拉普拉斯算子，且足够大。证明了该流将全测度集传递给全测度集。我们还讨论了一些简单的应用。这将Planchon - Visciglia和第二作者之前的结果从更高的维度扩展到了更高的维度。

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来源期刊

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.