报告题目：Ergodicity，exponential mixing and limit theorems of quasi-periodically forced 2D stochastic Navier-Stokes Equations in the hypoelliptic setting

报告人： 四川大学 吕克宁 教授

报告时间：2024年3月26日,  14：30-17：30

腾讯会议ID：586-326-571

Abstract：We consider the incompressible 2D Navier-Stokes equations on the torus driven by a deterministic time quasi-periodic force and a noise that is white in time and degenerate in Fourier space. We show that the asymptotic statistical behavior is characterized by a quasi-periodic invariant measure that exponentially attracts the law of all solutions. The result is true for any value of the viscosity $\nu>0$ and does not depend on the strength of the external forces.

By utilizing this quasi-periodic invariant measure, we establish a quantitative version of the strong law of large numbers and central limit theorem for the continuous time inhomogeneous solution processes with explicit convergence rates. It turns out that the convergence rate in the central limit theorem depends on the time inhomogeneity through the Diophantine approximation property on the quasi-periodic frequency of the quasi-periodic force.

We also establish a Donsker-Varadhan type large deviation principle with a nontrivial good rate function for the occupation measures of the time periodic inhomogeneous solution processes. This is a joint work with Liu Rongchang.

个人简介：吕克宁教授是微分方程与无穷维动力系统专家，曾任Brigham Young University和Michigan State University教授，现任四川大学教授、数学学院学术院长、中国数学会副理事长，2005年获得国家杰出青年科学基金(B类)，2010年入选国家海外高层次人才计划、2017年获首届“张芷芬数学奖”，2020年入选AMS fellow，先后主持国家自然科学基金重点项目（2014-2018）和国家自然科学基金重大项目（2021-2025）等，现任国际学术刊物《Journal of Differential Equations》共同主编，在不变流形和不变叶层、Sinai-Ruelle-Bowen测度、熵和Lyapunov指数以及随机动力系统的光滑共轭理论和偏微分方程的动力学等方面做出了多个原创性工作，相关论文发表在《Inventiones Mathematicae》、《Communications on Pure and Applied Mathematics》、《Memoirs of the American Mathematical Society》、《Archive for Rational Mechanics and Analysis》、《Annals of Probability》等学术期刊上。