Well-posedness and large deviations for 2D stochastic Navier–Stokes equations with jumps

Under the classical local Lipschitz and one sided linear growth assumptions on the coefficients of the stochastic perturbations, we first prove the existence and the uniqueness of a strong (in both the probabilistic and PDEs sense) solution to the 2-D Stochastic Navier-Stokes equations driven by multiplicative L\'evy noise. Applying the weak convergence method introduced by [19,18] for the case of the Poisson random measures, we establish a Freidlin-Wentzell type large deviation principle for the strong solution in PDE sense.