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We prove that every Markov solution to the three dimensional Navier-Stokesequation with periodic boundary conditions driven by additive Gaussian noise isuniquely ergodic. The convergence to the (unique) invariant measure isexponentially fast.  Moreover, we give a well-posedness criterion for the equations in terms ofinvariant measures. We also analyse the energy balance and identify the termwhich ensures equality in the balance.

Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise