Stochastic 2D hydrodynamical systems: Wong-Zakai approximation and Support theorem
Probability
2011-09-19 v2
Abstract
We deal with a class of abstract nonlinear stochastic models with multiplicative noise, which covers many 2D hydrodynamical models including the 2D Navier-Stokes equations, 2D MHD models and 2D magnetic B\'enard problems as well as some shell models of turbulence. Our main result describes the support of the distribution of solutions. Both inclusions are proved by means of a general Wong-Zakai type result of convergence in probability for non linear stochastic PDEs driven by a Hilbert-valued Brownian motion and some adapted finite dimensional approximation of this process.
Keywords
Cite
@article{arxiv.0907.2100,
title = {Stochastic 2D hydrodynamical systems: Wong-Zakai approximation and Support theorem},
author = {Igor Chueshov and Annie Millet},
journal= {arXiv preprint arXiv:0907.2100},
year = {2011}
}