Well-posedness and large deviations for 2D stochastic Navier–Stokes equations with jumps
Zdzisław Brzeźniak, Xuhui Peng, Jianliang Zhai
Source abstract
The aim of this paper is threefold. Firstly, we prove the existence and uniqueness of a global strong (in both the probabilistic and the PDE senses) \mathrm{H}^{1}_2 -valued solution to the 2D stochastic Navier–Stokes equations (SNSEs) driven by a multiplicative Lévy noise under the natural Lipschitz condition 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 wellposedness 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 by Budhiraja et al. (2011, 2013).
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