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，美国杨伯翰大学教授，美国数学会会士。从事无穷维动力系统的研究，已发表论文80余篇，发表期刊包括《Inventiones mathematicae》《Communications on Pure and Applied Mathematics》、《Memoirs of the American Mathematical Society》《Archive for Rational Mechanics and Analysis》《Journal of Differential Equations》。现任《Journal of Differential Equations》共同主编。

五、邀请人：

司文 数学学院副教授

六、时间：

4月28日（周四）15:00-16:00

七、地点：

腾讯会议

八、联系人

司文，联系方式：siwenmath@sdu.edu.cn

九、主办方：

山东大学数学学院