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Exponential mixing for 2D Navier-Stokes equations perturbed by an unbounded noise. (English) Zbl 1095.35032
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.

##### MSC:
 35Q30 Navier-Stokes equations 35R60 PDEs with randomness, stochastic partial differential equations 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60J05 Discrete-time Markov processes on general state spaces
##### Keywords:
Navier-Stokes equations; exponential mixing; coupling
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