Exponential mixing for 2D Navier-Stokes equations perturbed by an unbounded noise (Q813903)

The paper is devoted to the Dirichlet boundary problem for the two-dimensional Navier-Stokes equation perturbed by an unbounded kick force of the form \(\eta(t, x)=\sum_{k=1}^\infty \eta_k(x)\delta(t-k)\), where \(\delta(t)\) is the Dirac measure and \(\eta_k\) are i.i.d. random variables with range in the space of square integrable vector fields. The main result consists in the exponential convergence of any solution to the stationary measure in the dual Lipschitz norm. It is shown that this result can be derived from the existence of a coupling operator.