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

被引：10
作者：
Brzezniak, Zdzislaw [1 ]
Peng, Xuhui [2 ]
Zhai, Jianliang [3 ]
机构：
[1] Univ York, Dept Math, York YO10 5DD, England
[2] Hunan Normal Univ, Sch Math & Stat, MOE LCSM, Changsha 410081, Hunan, Peoples R China
[3] Univ Sci & Technol China, Sch Math Sci, CAS Wu Wen Tsun Key Lab Math, Hefei 230026, Anhui, Peoples R China
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2023年 / 25卷 / 08期
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
2D stochastic Navier-Stokes equations; Levy processes; Girsanov theorem; strong solutions in the probabilistic and PDE senses; Freidlin-Wentzell-type large deviation principle; PARTIAL-DIFFERENTIAL-EQUATIONS; NONLINEAR SCHRODINGER-EQUATION; ORNSTEIN-UHLENBECK PROCESSES; EVOLUTION-EQUATIONS; TIME REGULARITY; HYDRODYNAMICAL SYSTEMS; HEAT-EQUATION; LEVY NOISE; DRIVEN; MARTINGALE;
D O I：
10.4171/JEMS/1214
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 Levy 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).
引用
收藏
页码：3093 / 3176
页数：84
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