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Large Deviations and Averaging for Stochastic Tamed 3D Navier–Stokes Equations with Fast Oscillations

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Abstract

In this paper, we first study the strong averaging principle for stochastic tamed 3D Navier–Stokes equation with fast oscillations, which can be viewed as the functional law of large numbers. Furthermore, in order to investigate the probability of deviations away from the limiting process, the Freidlin–Wentzell type large deviation principle is also established by employing the weak convergence method.

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Acknowledgements

The authors would like to thank the referees for their very constructive suggestions and valuable comments. The research of W. Hong is supported by NSFC (No. 12171354). The research of S. Li is supported by NSFC (No. 12001247, 11931004), NSF of Jiangsu Province (No. BK20201019), NSF of Jiangsu Higher Education Institutions of China (No. 20KJB110015). The research of W. Liu is supported by NSFC (No. 12171208, 11831014, 12090011) and the PAPD of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, China

    Wei Hong

  2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China

    Miaomiao Li, Shihu Li & Wei Liu

  3. RIMS, Jiangsu Normal University, Xuzhou, 221116, China

    Wei Liu

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  1. Wei Hong
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Hong, W., Li, M., Li, S. et al. Large Deviations and Averaging for Stochastic Tamed 3D Navier–Stokes Equations with Fast Oscillations. Appl Math Optim 86, 15 (2022). https://doi.org/10.1007/s00245-022-09895-8

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