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- Title
Well-posedness and large deviations for 2D stochastic Navier--Stokes equations with jumps.
- Authors
Brzézniak, Zdzisław; Xuhui Peng; Jianliang Zhai
- 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) H¹2-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).
- Subjects
NAVIER-Stokes equations; LIPSCHITZ spaces; POISSON processes; STOCHASTIC analysis; DEVIATION (Statistics)
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2023, Vol 25, Issue 8, p3093
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1214