Seminar on Stochastic Differential Equations and Applications

Date: 

Wednesday, 8 August 2007 - 2:00pm to 4:00pm

Venue: 

Red Centre- Room 3085

We put forward a tamed scheme for 3D Navier-Stokes equation, and prove the existence of a unique smooth solution to the determinstic and stochastic tamed 3D Navier-Stokes equation in the whole space as well as in the periodic boundary case. The main feature of this scheme is that if there exists a bounded solution to the classical 3D NSE, then this solution satisfies our tamed equation. Moreover, in the case of periodic boundary and degenerated additive noise, using the notion of asymptotic strong Feller property proposed by Hairer and Mattingly, we prove the uniqueness of invariant measure for the corresponding transition semigroup.