一、题目

Ergodicity, mixing, limit theorems for quasi-periodically forced 2D stochastic Navier-Stokes Equations

二、主讲人

吕克宁

三、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 extremely degenerate in Fourier space. We show that the asymptotic statistical behavior is characterized by a uniquely ergodic  and exponentially mixing quasi-periodic invariant measure. The result is true for any value of the viscosity $\nu>0$. By utilizing this quasi-periodic invariant measure, we show the strong law of large numbers and central limit theorem for the continuous time inhomogeneous solution processes. Estimates of the corresponding rate of convergence are also obtained, which is the same as in the time homogeneous case for the strong law of large numbers, while the convergence rate in the central limit theorem depends on the Diophantine approximation property on the quasi-periodic frequency and the mixing rate of the quasi-periodic invariant measure.  We also prove the existence of a stable quasi-periodic solution in the laminar case (when the viscosity is large). This talk is based on a joint work with Liu Rongchang.

四、主讲人简介

吕克宁教授是微分方程与无穷维动力系统专家，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联合主编。研究方向包括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等方面。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。

五、时间

7月28日（周四）15:00

六、地点

华岗苑东楼119报告厅

腾讯会议：240 749 212

会议密码：123456

七、主办

非线性期望前沿科学中心

数学与交叉科学研究中心