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Stochastic 2D hydrodynamical type systems: well posedness and large deviations. (English) Zbl 1196.49019
Summary: 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.

MSC:
49K40 Sensitivity, stability, well-posedness
93E20 Optimal stochastic control
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