Markov solutions for the 3D stochastic Navier--Stokes equations with state dependent noise
Analysis of PDEs
2007-05-23 v2 Numerical Analysis
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].
Cite
@article{arxiv.math/0512361,
title = {Markov solutions for the 3D stochastic Navier--Stokes equations with state dependent noise},
author = {Arnaud Debussche and Cyril Odasso},
journal= {arXiv preprint arXiv:math/0512361},
year = {2007}
}