Speaker：Kening Lv (Sichuan University)

Time：2023-11-25, 8:40

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:

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.