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Markov solutions for the 3D stochastic Navier--Stokes equations with state dependent noise

Arnaud Debussche·Cyril Odasso
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Abstract

We construct a Markov family of solutions for the 3D Navier-Stokes equation perturbed by a non degenerate noise. We improve the result of [DPD-NS3D] 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 [DPD-NS3D].

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Arnaud Debussche, Cyril Odasso. 2005-12-15. Markov solutions for the 3D stochastic Navier--Stokes equations with state dependent noise. https://arxiv.org/abs/math/0512361

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