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

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

2009-07-13

arxiv.org/abs/0907.2100v2

Stochastic Analysis and Applications 29, 4 (2011) 570-611

Mathematics

Probability

Scientific paper

10.1080/07362994.2011.581081

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.

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