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Well-posedness and large deviations for 2D stochastic Navier--Stokes equations with jumps.
- Source :
- Journal of the European Mathematical Society (EMS Publishing); 2023, Vol. 25 Issue 8, p3093-3176, 84p
- Publication Year :
- 2023
-
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) H¹<subscript>2</subscript>-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). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14359855
- Volume :
- 25
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Journal of the European Mathematical Society (EMS Publishing)
- Publication Type :
- Academic Journal
- Accession number :
- 164755477
- Full Text :
- https://doi.org/10.4171/JEMS/1214