THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

doi:10.1007/s10473-024-0311-z

Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (3): 973-983.doi: 10.1007/s10473-024-0311-z

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THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

Cuntao xiao¹, Hua qiu^2,*, Zheng-an yao³

1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510090, China;
2. Department of Mathematics, South China Agricultural University, Guangzhou 510642, China;
3. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Received:2022-07-08 Revised:2022-11-25 Online:2024-06-25 Published:2024-05-21
Contact: *Hua qiu, E-mail:tsiuhua@scau.edu.cn
About author:Cuntao xiao,E-mail:xiaocuntao@gdut.edu.cn; Zheng-an yao ,E-mail:mcsyao@mail.sysu.edu.cn
Supported by:
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).

Abstract

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.

Key words: regularized MHD equations, fractional Laplacian, global well-posedness, analyticity, decay rate

CLC Number:

35B65

Cuntao xiao, Hua qiu, Zheng-an yao. THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS[J].Acta mathematica scientia,Series B, 2024, 44(3): 973-983.

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THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

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