Wong Zakai approximation for 2D hydrodynamical stochastic evolution equations

Annie Millet (1, 2) , Igor Chueshov (3)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 Department of Mechanics and Mathematics

We describe the support of the distribution for 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. Both inclusions are proved by means of a general Wong--Zakai type result of convergence in probability for nonlinear stochastic PDEs driven by a Hilbert-valued Brownian motion and some adapted finite dimensional approximation of this process.

Mots clés: Wonz Zakai approximation; support theorem; 2D Navier Stokes equations; stochastic controlled equation

Domaines: Probabilités [math.PR]

Annie Millet, Igor Chueshov. Wong Zakai approximation for 2D hydrodynamical stochastic evolution equations. Evolution Equations: Randomness and Asymptotics, Oct 2011, Bad Herrenalb, Germany. ⟨hal-00624585⟩