Well-posedness and large deviations for a class of SPDEs with Lévy noise

In this paper, a class of stochastic partial differential equations (SPDEs) with Lévy noise is concerned. Firstly, the local well-posedness is established by the iterative approximation. Then the large deviation principle (LDP) for the regularized SPDEs is obtained by the weak convergence approach. To get the LDP for SPDEs here, an exponential equivalence of the probability measures is proved. The results can be applied to some types of SPDEs such as stochastic Burgers equation, stochastic b-family equation, stochastic modified Novikov equation and stochastic μ-Hunter-Saxton equation.