Abstract.
We construct a Markov family of solutions for the 3D Navier-Stokes equations perturbed by a non degenerate noise. We improve the result of [3] in two directions. We see that in fact not only a transition semigroup but a Markov family of solutions can be constructed. Moreover, we consider a state dependant noise. Another feature of this work is that we greatly simplify the proofs of [3].
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Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday
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Debussche, A., Odasso, C. Markov solutions for the 3D stochastic Navier–Stokes equations with state dependent noise. J. evol. equ. 6, 305–324 (2006). https://doi.org/10.1007/s00028-006-0254-y
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DOI: https://doi.org/10.1007/s00028-006-0254-y