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Regularization by transport noises for 3D MHD equations

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Abstract

We consider the problem of regularization by noises for the three-dimensional magnetohydrodynamical (3D MHD) equations. It is shown that in a suitable scaling limit, the multiplicative noise of transport type gives rise to bounds on the vorticity fields of the fluid velocity and magnetic fields. As a result, if the noise intensity is big enough, then the stochastic 3D MHD equations admit a pathwise unique global solution for large initial data with high probability.

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Acknowledgements

This work was supported by the National Key R&D Program of China (Grant No. 2020YFA0712700), National Natural Science Foundation of China (Grant Nos. 11931004 and 12090014) and the Youth Innovation Promotion Association, Chinese Academy of Sciences (Grant No. Y2021002). The author thanks the referees for helpful comments on the first version of this paper.

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  1. Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Dejun Luo

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Dejun Luo

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  1. Dejun Luo
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Luo, D. Regularization by transport noises for 3D MHD equations. Sci. China Math. 66, 1375–1394 (2023). https://doi.org/10.1007/s11425-021-1981-9

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