Stochastic 2D hydrodynamical systems: Wong-Zakai approximation and Support theoremReport as inadecuate




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

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 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.

Keywords : Hydrodynamical models MHD Bénard convection shell models of turbulence stochastic PDEs Wong-Zakai approximations support theorem





Author: Igor Chueshov - Annie Millet -

Source: https://hal.archives-ouvertes.fr/



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