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

Zdzislaw Brzezniak, Xuhui Peng, Jianliang Zhai

Research output: Contribution to journalArticlepeer-review

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) 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 [16][18].
Original languageEnglish
Pages (from-to)3093-3176
Number of pages84
JournalJournal of the european mathematical society
Volume25
Issue number8
DOIs
Publication statusPublished - 3 Sept 2022

Bibliographical note

© 2022 European Mathematical Society

Cite this