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

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.

References in corpus (2)

• Stochastic 2D hydrodynamical type systems: Well posedness and large deviations
• Large deviations for the Boussinesq Equations under Random Influences

Cited by in corpus (4)

• On the rate of convergence of the 2-D stochastic Leray-$\alpha$ model to the 2-D stochastic Navier-Stokes equations with multiplicative noise
• The support of singular stochastic PDEs
• Time Discrete Approximation of Weak Solutions for Stochastic Equations of Geophysical Fluid Dynamics and Applications
• A support theorem for parabolic stochastic PDEs with nondegenerate Hölder diffusion coefficients