应西北师范大学数学与统计学院邀请，四川大学吕克宁教授将为我院师生作线上学术报告。
报告题目：Exponential mixing and limit theorems of quasi-periodically forced
2D stochastic Navier-Stokes Equations in the hypoelliptic setting
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 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.
报告时间：2023年11月28日8:00
报告地点：腾讯会议(ID：136 669 464)
邀请人：陈鹏玉 教授 张旭萍 副教授
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报告人简介
吕克宁教授是微分方程与无穷维动力系统领域的国际知名专家，曾任Brigham Young University和Michigan State University教授，现任四川大学教授。2017年获首届“张芷芬数学奖”，2020年入选AMS fellow，现任国际学术刊物JDE共同主编。他在不变流形和不变叶层，Sinai-Ruelle-Bowen测度，熵和Lyapunov指数以及随机动力系统的光滑共轭理论和随机偏微分方程的动力学方面做出了多个重要工作，相关论文发表在《Inventiones Mathematicae》、《Communications on Pure and Applied Mathematics》、《Memoirs of the American Mathematical Society》、《Advances in Mathematics》等学术期刊上。
甘肃省数学与统计学基础学科研究中心
数学与统计学院
2023年11月24日
