Exponential mixing and limit theorems of quasi-periodically forced 2D stochastic Navier-Stokes Equations in the hypoelliptic setting

：吕克宁（四川大学）
：2023-11-25 08:40
：Conference Room 105 at Experiment Building at Haiyun Campus

报告人：吕克宁（四川大学）

时  间：2023年11月25日8:40

地  点：海韵园实验楼105报告厅

内容摘要:

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，2017年获首届“张芷芬数学奖”，2020年入选AMS fellow，现任国际学术刊物JDE共同主编。他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随机偏微分方程的动力学方面做出了多个工作，相关论文发表在《Inventiones mathematicae》、《Communications on Pure and Applied Mathematics》、《Memoirs of the American Mathematical Society》等学术期刊上。

 

联系人：吴伟胜