Abstract
The current paper is devoted to the stochastic tamed 3D Naiver-Stokes equation with degenerate noise with degenerate random forcing. We prove that the associated Markov semigroup possesses an exponentially attracting invariant measure by showing that the corresponding dynamical system possesses a strong type of Lyapunov structure along with a special type of gradient inequality and is of a relatively weak form of irreducibility.
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