Summary
We prove the existence of martingale solutions and of stationary solutions of stochastic Navier-Stokes equations under very general hypotheses on the diffusion term. The stationary martingale solutions yield the existence of invariant measures, when the transition semigroup is well defined. The results are obtained by a new method of compactness.
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Flandoli, F., Gatarek, D. Martingale and stationary solutions for stochastic Navier-Stokes equations. Probab. Th. Rel. Fields 102, 367–391 (1995). https://doi.org/10.1007/BF01192467
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DOI: https://doi.org/10.1007/BF01192467