应304am永利集团官网院长李万同教授邀请，美国杨伯翰大学（Brigham Young University）吕克宁教授将于2022年4月27日-4月28日与我校有关师生进行在线学术研讨，其中4月28日举行线上专题学术报告。

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

时 间： 4月28日上午10:00

腾讯会议ID：755 292 205

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.

吕克宁教授简介

吕克宁，现任美国杨伯翰大学教授，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《Invent. Math.》、《Comm. Pure Appl. Math.》、《Mem. Amer. Math. Soc.》、《Arch. Rational Mech. Anal.》、《Adv. Math.》。现任《Journal of Differential Equations》共同主编。

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萃英学院

2022年4月27日