The Exponential Behaviour and Stabilizability of Stochastic 2D-Navier–Stokes Equations

Abstract

Some results on the pathwise exponential stability of the weak solutions to a stochastic 2D-Navier–Stokes equation are established. The first ones are proved as a consequence of the exponential mean square stability of the solutions. However, some of them are improved by avoiding the previous mean square stability in some more particular and restrictive situations. Also, some results and comments concerning the stabilizability and stabilization of these equations are stated.