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The global existence and analyticity of a mild solution to the 3D regularized MHD equations

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Abstract

In this paper, we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms. We establish the global existence of mild solutions to this system with small initial data. In addition, we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, 510090, China

    Cuntao Xiao

  2. Department of Mathematics, South China Agricultural University, Guangzhou, 510642, China

    Hua Qiu

  3. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Zheng-an Yao

Authors
  1. Cuntao Xiao
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  2. Hua Qiu
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  3. Zheng-an Yao
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Corresponding author

Correspondence to Hua Qiu.

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Conflict of Interest The authors declare no conflict of interest.

Additional information

Xiao’s work was supported by the Opening Project of Guangdong Province Key Laboratory of Cyber-Physical System (2016B030301008); Qiu’s work was supported by the National Natural Science Foundation of China (11126266), the Natural Science Foundation of Guangdong Province (2016A030313390), the Quality Engineering Project of Guangdong Province (SCAU-2021-69), and the SCAU Fund for High-level University Building; Yao’s work was supported by the National Key Research and Development Program of China(2020YFA0712500) and the National Natural Science Foundation of China (11971496, 12126609).

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Xiao, C., Qiu, H. & Yao, Za. The global existence and analyticity of a mild solution to the 3D regularized MHD equations. Acta Math Sci 44, 973–983 (2024). https://doi.org/10.1007/s10473-024-0311-z

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  • DOI: https://doi.org/10.1007/s10473-024-0311-z

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