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

2019/08/17 by Brzezniak, Zdzislaw, Peng, Xuhui, Zhai, Jianliang · 1 citation
#60F10 #60H15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1908.06228

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].

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• McKean-Vlasov SPDEs driven by Poisson random measure: Well-posedness and large deviation principle

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