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Global Well-Posedness of Stochastic 3D Primitive Equations with Anticipating Initial Data

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Abstract

In this article, we consider 3D stochastic primitive equations (PEs) driven by affine-linear multiplicative white noise, with random initial condition. Our main objective is to obtain the global well-posedness of the stochastic equations under the sufficient Malliavin regularity of the initial condition. Apart from the conventional strategy, we adopt the dynamical system approach and techniques from Malliavin calculus to attack the global well-posedness problem for the PEs.

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Acknowledgements

The authors are deeply grateful for the editor’s suggestions, which greatly broaden our horizon and improve the article in an extensive way. We also thank the refree for helpful comments on the first version of this article.

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Authors and Affiliations

  1. RCSDS, Academy of Mathematics and Systems Science, Chineses Academy of Sciences, Beijing, 100190, China

    Zhao Dong

  2. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, China

    Boling Guo

  3. School of Statistics and Data Science, Nankai University, Tianjin, 300071, China

    Lidan Wang

  4. School of Statistics and Mathematics, Chongqing University, Chongqing, 400044, China

    Guoli Zhou

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  1. Zhao Dong
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  3. Lidan Wang
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This work was partially supported by National Key R and D Program of China (No. 2020YFA0712700), NSFC (Nos. 11931004, 11971077, 12090014, 11801283), Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (No.2008DP173182), Chongqing Key Laboratory of Analytic Mathematics and Applications, Chongqing University, Natural Science Foundation Project of CQ (No. cstc2020jcyj-msxmX0441), Fundamental Research Funds for the Central Universities (Nos. 2020CDJ-LHZZ-027, 2022CDJXY-001).

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Dong, Z., Guo, B., Wang, L. et al. Global Well-Posedness of Stochastic 3D Primitive Equations with Anticipating Initial Data. J Dyn Diff Equat (2022). https://doi.org/10.1007/s10884-022-10211-9

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