Well-posedness and large deviations for 2-D Stochastic Navier-Stokes equations with jumps
Probability
2021-10-06 v3
Abstract
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) -valued solution to the 2D stochastic Navier-Stokes equations (SNSEs) driven by a multiplicative L\'evy 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 [16][18].
Cite
@article{arxiv.1908.06228,
title = {Well-posedness and large deviations for 2-D Stochastic Navier-Stokes equations with jumps},
author = {Zdzislaw Brzezniak and Xuhui Peng and Jianliang Zhai},
journal= {arXiv preprint arXiv:1908.06228},
year = {2021}
}