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This article is devoted to the large deviation principle for a wide class of stochastic hydrodynamical systems driven by multiplicative Lévy noise. The model covers many equations arising form fluid dynamics such as 2D Navier-Stokes equations, 2D MHD models and the 2D magnetic Bénard problem and also shell models of turbulence. The main difficulty in proving the large deviation principle for the system is overcame by using the weak convergence method introduced by Budhiraja, Dupuis and Maroulas (Ann. Probab. 36: 1390–1420, 2008 and Annales De L Institut Henri Poincare. 47: 725–747, 2011). [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of a random attractor, the finiteness of its fractal dimension, the random squeezing property, and the existence of a finite number of determining modes for an abstract stochastic 2D hydrodynamical type equations with additive white noise. [ABSTRACT FROM AUTHOR]

We study the exponential behaviour and stabilizability of the following abstract nonlinear stochastic evolution equation whereis a multiplicative white noise in time with spatial correlation. Applications to concrete models in fluid mechanics are also given. [ABSTRACT FROM PUBLISHER]