應77779193永利邀請，四川大學呂克甯教授将為我院師生作線上學術報告。
報告題目：Exponential mixing and limit theorems of quasi-periodically forced
2D stochastic Navier-Stokes Equations in the hypoelliptic setting
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 degenerate in Fourier space. We show that the asymptotic statistical behavior is characterized by a quasi-periodic invariant measure that exponentially attracts the law of all solutions. The result is true for any value of the viscosity $\nu>0$ and does not depend on the strength of the external forces.By utilizing this quasi-periodic invariant measure, we establish a quantitative version of the strong law of large numbers and central limit theorem for the continuous time inhomogeneous solution processes with explicit convergence rates. It turns out that the convergence rate in the central limit theorem depends on the time inhomogeneity through the Diophantine approximation property on the quasi-periodic frequency of the quasi-periodic force. We also establish a Donsker-Varadhan type large deviation principle with a nontrivial good rate function for the occupation measures of the time periodic inhomogeneous solution processes. This is a joint work with Liu Rongchang.
報告時間：2023年11月28日8:00
報告地點：騰訊會議(ID：136 669 464)
邀請人：陳鵬玉 教授 張旭萍 副教授
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報告人簡介
呂克甯教授是微分方程與無窮維動力系統領域的國際知名專家，曾任Brigham Young University和Michigan State University教授，現任四川大學教授。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重要工作，相關論文發表在《Inventiones Mathematicae》、《Communications on Pure and Applied Mathematics》、《Memoirs of the American Mathematical Society》、《Advances in Mathematics》等學術期刊上。
甘肅省數學與統計學基礎學科研究中心
77779193永利
2023年11月24日
