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Stochastic 2D hydrodynamical systems: Wong-Zakai approximation and Support theorem

By Igor Chueshov and Annie Millet

Abstract

International audienceWe 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 Bénard 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

Topics: Hydrodynamical models, MHD, Bénard convection, shell models of turbulence, stochastic PDEs, Wong-Zakai approximations, support theorem, Primary 60H15, 60F10 ; Secondary 76D06, 76M35, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Publisher: Taylor & Francis: STM, Behavioural Science and Public Health Titles
Year: 2011
DOI identifier: 10.1080/07362994.2011.581081
OAI identifier: oai:HAL:hal-00403685v2
Provided by: Hal-Diderot

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