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[Under suitable assumptions of regularity and non-degeneracy on the covariance of the driving additive noise, any Markov solution to the stochastic Navier-Stokes equations has an associated generator of the diffusion and is the unique solution to the corresponding martingale problem. Some elementary examples are discussed to interpret these results.]
Published: Feb 4, 2011
Keywords: Stochastic Navier-Stokes equations; martingale problem; Markov property; Markov solutions; strong Feller property; well-posedness; invariant measures.
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