关于举行吕克宁教授（四川大学）学术报告会的通知

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

报 告人：吕克宁 教授（四川大学）

报告时间：2022年5月11日（星期三）上午9:00-- 11:00             

报告地点：腾讯会议：311-273-145，密码：220511

邀 请人：曾才斌 副教授

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数学学院

2022年5月10日

报告摘要：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.

报告人简介：吕克宁，美国杨伯翰大学教授，美国数学会会士，研究方向为无穷维动力系统、非线性偏微分方程、随机偏微分方程，已发表论文近百篇，发表期刊包括《Invent. Math.》、《Comm. Pure Appl. Math.》、《Mem. Amer. Math. Soc.》、《Arch. Rational Mech. Anal.》、《Adv. Math.》。现任《J. Differential Equations》共同主编。