Seminar: Mixing and chaotic behavior of random dynamical systems via controllability

发布部门：行政办公室(A) 浏览次数：10

Seminar| Institute of Mathematical Sciences

Time: Wednesday, December 3th, 2025,16:00-17:00

Location: RS408, IMS

Speaker: Vahagn Nersesyan (NYU Shanghai)

Abstract: The problem of ergodicity and chaotic behavior of randomly forced dissipative PDEs has attracted a lot of attention in the last twenty years. It is well understood that if all or sufficiently many Fourier modes of the PDE are directly perturbed by the noise, then the problem has a unique stationary measure which is exponentially stable in an appropriate metric. The case when the random perturbation acts directly only on a few Fourier modes is much less understood and is the main subject of this talk. We will explain how the controllability properties of the underlying deterministic system can be used to study the ergodic and chaotic behavior of the random dynamics. The results will be illustrated through the example of 2D Navier-Stokes equations; however, the methods apply to a wide variety of systems as soon as they satisfy appropriate controllability conditions.

About the speaker: Vahagn Nersesyan is an Associate Professor of Mathematics at NYU Shanghai and an Associated Professor at the Courant Institute of Mathematics at NYU. He obtained his Ph.D. from the University of Paris Sud and was a Maître de conferences at the University of Paris-Saclay (Versailles campus) until 2021. His main research interests are in the intersection of Partial Differential Equations and Probability.