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Global weighted regularity for the 3D axisymmetric MHD equations

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Abstract

In this paper, we study the three-dimensional axisymmetric incompressible magnetohydrodynamic (MHD) equations with nonzero swirl. By using symmetric properties of the Riesz transform and Hardy–Sobolev inequalities, we establish some new weighted regularity criteria via partial components of velocity and magnetic fields.

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Acknowledgements

The authors would like to thank Professors Hui Chen and Zujin Zhang for their kind help and comments and thank the anonymous referees for their suggestions which make the paper more readable. Guo was partially supported by the Natural Science Foundation of Jiangsu Province (Grant No. BK20201478) and the Qinglan Project of Jiangsu Universities. Li was supported in part by the Natural Science Foundation of China (Grant No. 12171258).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huaiyin Normal University, Huaian, 223300, People’s Republic of China

    Zhengguang Guo

  2. Department of Mathematics, Wenzhou University, Wenzhou, 325035, People’s Republic of China

    Yufei Wang

  3. School of Sciences, Nantong University, Nantong, 226019, People’s Republic of China

    Yeping Li

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  1. Zhengguang Guo
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Guo, Z., Wang, Y. & Li, Y. Global weighted regularity for the 3D axisymmetric MHD equations. Z. Angew. Math. Phys. 73, 174 (2022). https://doi.org/10.1007/s00033-022-01815-8

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  • DOI: https://doi.org/10.1007/s00033-022-01815-8

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