| In this paper,large deviation principle is established for the 2D stochastic magnetohydrodynamic equations driven by jump–type Lévy processes,i.e.(?)Firstly,using the functional representation of the operators,the stochastic 2D magnetohydrodynamic(MHD)equations driven by the jump-type Lévy process are written in a form of abstract evolution equation.Then,based on the assump-tions of noise and noise coefficients,the method of Galerkin approximation is used to obtain the well-posedness of the solution of the deterministic integral equation derived from the abstract evolution equation of the 2D stochastic MHD equations driven by the jump-type Lévy process.According to the results of Budhiraja and Dupuis,if the base space is a Polish space,then the large deviation principle is equivalent to the Laplace-Varadhan principle.And then a small perturbation is added to the 2D stochastic MHD equation driven by the jump-type Lévy process.Based on the weak convergence approach,then using a variational representation for the non-negative functional of general Poisson random measures and Brownian motions,the weak convergence criterion of the large deviation principle is verified,namely the two sufficient conditions for the large deviation principle to hold.Fi-nally,a Freidlin-Wentzell type large deviation principle for strong solutions of the 2D stochastic MHD equations driven by jump-type Lévy process was established in an appropriate Polish space. |
