Analysis of Equilibrium States of Markov Solutions to the 3d Navier-stokes Equations Driven by Additive Noise
نویسندگان
چکیده
We prove that every Markov solution to the three dimensional Navier-Stokes equation with periodic boundary conditions driven by additive Gaussian noise is uniquely ergodic. The convergence to the (unique) invariant measure is exponentially fast. Moreover, we give a well-posedness criterion for the equations in terms of invariant measures. We also analyse the energy balance and identify the term which ensures equality in the balance.
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