應yl7703永利官網(wǎng)院長李萬同教授邀請，美國楊伯翰大學（Brigham Young University）呂克寧教授將于2022年4月27日-4月28日與我校有關師生進行在線學術(shù)研討，其中4月28日舉行線上專題學術(shù)報告。

報告題目: Ergodicity, mixing, limit theorems for quasi-periodically forced 2D stochastic Navier-Stokes Equations

時 間： 4月28日上午10:00

騰訊會議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.

呂克寧教授簡介

呂克寧，現(xiàn)任美國楊伯翰大學教授，從事無窮維動力系統(tǒng)的研究，已發(fā)表論文80余篇，發(fā)表期刊包括《Invent. Math.》、《Comm. Pure Appl. Math.》、《Mem. Amer. Math. Soc.》、《Arch. Rational Mech. Anal.》、《Adv. Math.》?，F(xiàn)任《Journal of Differential Equations》共同主編。

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萃英學院

2022年4月27日