Ergodicity for 2D stochastic Navier-Stokes equations on the whole space

Abstract: In this seminar, first I will discuss the theory of global attractors for dynamical systems. By motivating some examples, I will discuss the generalization of global attractors into random attractors for random dynamical systems (RDS). Next, we will see the sufficient and necessary criteria for the existence of random attractors for non-compact RDS. We will apply the above-mentioned theory to 2D stochastic Navier-Stokes equations (SNSE) driven by a linear multiplicative white noise and defined on the whole space R^2 to find the existence of random attractors. As a consequence of the existence of random attractors, we will discuss the existence of an invariant measure for the RDS associated with 2D SNSE. Finally, we will discuss the uniqueness of invariant measures for zero external forcing by using the linear multiplicative structure of the noise coefficient and exponential stability of solutions.

Zoom Link:

https://zoom.us/j/97443614179?pwd=d3V1SXViR1NoVUtNUTd1N1p4WVF3UT09 

ID: 974 4361 4179 

passcode: 855648