Large deviation principle for a class of stochastic hydrodynamical type systems driven by multiplicative Lévy noises

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).