報告題目：Ergodicity, mixing, limit theorems for quasi-periodically forced 2D stochastic Navier-Stokes Equations
報 告 人： 呂克甯 教授 四川大學
報告時間： 2023年5月27日 14：30-15：30
報告地點： 數學樓三樓多功能廳1
校内聯系人：韓月才 hanyc@jlu.edu.cn
報告摘要：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.
報告人簡介： 呂克甯，微分方程與無窮維動力系統專家，曾任Brigham Young University和Michigan State University教授，現任四川大學教授、博士生導師，2017年獲首屆“張芷芬數學獎”，2020年入選AMS fellow，現任國際學術刊物JDE共同主編。他在不變流形和不變葉層，Sinai-Ruelle-Bowen測度，熵和Lyapunov指數以及随機動力系統的光滑共轭理論和随機偏微分方程的動力學方面做出了多個工作，相關論文發表在《Inventiones mathematicae》、《Communications on Pure and Applied Mathematics》、《Memoirs of the American Mathematical Society》等學術期刊上。
