中国科学院数学与系统科学研究院

数学研究所

中国科学院华罗庚数学重点实验室

华罗庚青年数学论坛

综合报告

报告人： 孙晨旻 博士 （Université Paris Est Créteil, France）

题  目：Transport properties of Gaussian measures for nonlinear Schrödinger equations

时  间：2023.11.10（星期五），15:00-16:00

地  点：Zoom会议：897 6959 5381  密码：1110

摘  要：In the statistical study of Hamiltonian PDEs out of the equilibrium (lack of invariant measures), it is a natural question to understand the transport properties for canonical Gaussian measures. The first question is to understand whether Gaussian measures arequasi-invariant, i.e. Gaussian measures push-forward by the flow are equivalent to the original ones. Once we know the Gaussian measures are quasi-invariant, we would like also to understand the property of their Radon-Nikodym densities.  

In this colloquium talk, I will review some recent development in this direction for nonlinear Schrödinger equations. More precisely, I will explain several strategies of proving quasi-invariant property as well as a consequence of quantitative quasi-invariantproperty. This talk is based on a joint-paper with Nikolay Tzvetkov, and some ongoing projects.