Stochastic 2D hydrodynamical type systems: Well posedeness and large deviations (original) (raw)

We deal with a class of abstract nonlinear stochastic models, which covers many 2D hydrodynamical models including 2D Navier-Stokes equations, 2D MHD models and the 2D magnetic Bénard problem and also some shell models of turbulence. We state the existence and uniqueness theorem for the class considered. Our main result is a Wentzell-Freidlin type large deviation principle for small multiplicative noise which we prove by a weak convergence method. Keywords Hydrodynamical models • MHD • Bénard convection • Shell models of turbulence • Stochastic PDEs • Large deviations The research of the second named author is partially supported by the research project BMF2003-01345.