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Global well-posedness and large deviations for 3D stochastic Burgers equations

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Abstract

In this paper, we study the stochastic vector-valued Burgers equations with non-periodic boundary conditions. We first apply a contraction principle argument to show local existence and uniqueness of a mild solution to this model. Then, toward obtaining the global well-posedness, we derive a priori estimates of the local solution by utilizing the maximum principle. Finally, we establish, by means of the weak convergence approach, the Freidlin–Wentzell type large deviation principle for 3D stochastic Burgers equations when the noise term goes to zero.

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Acknowledgements

This work was partially supported by NNSF of China (Grant Nos. 11971077, 11801032), Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (No. 2008DP173182), China Postdoctoral Science Foundation funded project (No. 2018M641204), Natural Science Foundation Project of CQ (Grant No. cstc2016jcyjA0326), Fundamental Research Funds for the Central Universities (Grant Nos. 2018CDXYST0024, 63181314) and China Scholarship Council (Grant No.201506055003). Last but not least, we should deeply appreciate the reviewers who read our article carefully and gave valuable suggestions that improve our paper greatly.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Rangrang Zhang

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

    Guoli Zhou

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

    Boling Guo

  4. Swansea University, Bay Campus Fabian Way, Swansea, SA1 8EN, Wales, UK

    Jianglun Wu

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  1. Rangrang Zhang
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  2. Guoli Zhou
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  3. Boling Guo
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  4. Jianglun Wu
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Correspondence to Guoli Zhou.

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Zhang, R., Zhou, G., Guo, B. et al. Global well-posedness and large deviations for 3D stochastic Burgers equations. Z. Angew. Math. Phys. 71, 30 (2020). https://doi.org/10.1007/s00033-020-1259-z

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  • DOI: https://doi.org/10.1007/s00033-020-1259-z

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