# Mathematical Sciences Research Institute

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# Seminar

Small Noise Asymptotics for the Stochastic 2D-Navier-Stokes Equation with Vanishing Noise Correlation November 10, 2021 (02:00 PM PST - 03:00 PM PST)
Parent Program: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Sandra Cerrai (University of Maryland)
Description No Description
Video

#### Small Noise Asymptotics For The Stochastic 2D-Navier-Stokes Equation With Vanishing Noise Correlation

Abstract/Media

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I will present a series of asymptotic results for the two-dimensional incompressible Navier-Stokes equation, driven by a Gaussian noise that is white in time and colored in space. I will consider the case when the magnitude of the random forcing $\sqrt{\e}$ and its correlation scale $\delta(\e)$ are both small. I will prove a large deviations principle for the solutions, as well as for the family of invariant measures, as $\e$ and $\delta(\e)$ are simultaneously sent to $0$, under a suitable scaling. I will also mention some results on the limiting behavior of the associated quasi-potential and on the exit problem.