The aim of this paper is threefold. Firstly, we prove the existence and the uniqueness of a global strong (in both the probabilistic and the PDE senses) H12-valued solution to the 2D stochastic Navier-Stokes equations (SNSEs) driven by a multiplicative Lévy noise under the natural Lipschitz on balls and linear growth assumptions on the jump coefficient. Secondly, we prove a Girsanov-type theorem for Poisson random measures and apply this result to a study of the well-posedness of the corresponding stochastic controlled problem for these SNSEs. Thirdly, we apply these results to establish a Freidlin-Wentzell-type large deviation principle for the solutions of these SNSEs by employing the weak convergence method introduced in papers .
|Journal||Journal of the european mathematical society|
|Publication status||Accepted/In press - 25 Sept 2021|