Existence of weak solutions to the 3D stochastic Navier-Stokes equations in the martingale sense is known, but their uniqueness is open as in the deterministic case. We prove the existence of selections with a weak form of Markov property. Under special assumptions on the noise, we prove the full Markov property and a form of continuous dependence on initial conditions, similar to the Strong Feller property. The methods are strongly inspired to an approach of Da Prato and Debussche.

Lecture #12197

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