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Global Well-posedness of Generalized Magnetohydrodynamics Equations in Variable Exponent Fourier-Besov-Morrey Spaces

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Abstract

A generalized incompressable magnetohydrodynamics system is considered in this paper. Furthermore, results of global well-posednenss are established with the aid of Littlewood–Paley decomposition and Fourier localization method in mentioned system with small initial condition in the variable exponent Fourier–Besov–Morrey spaces. Moreover, the Gevrey class regularity of the solution is also achieved in this paper.

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Acknowledgements

The authors would like to thank the anonymous referee for their careful reading of the paper and valuable suggestions.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, 321004, China

    Muhammad Zainul Abidin & Jie Cheng Chen

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  1. Muhammad Zainul Abidin
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  2. Jie Cheng Chen
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Correspondence to Muhammad Zainul Abidin.

Additional information

The Research was Supported by Zhejiang Normal University Postdoctoral Research fund under (Grant No. ZC304020909) and NSF of China (Grant No. 10271437)

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Abidin, M.Z., Chen, J.C. Global Well-posedness of Generalized Magnetohydrodynamics Equations in Variable Exponent Fourier-Besov-Morrey Spaces. Acta. Math. Sin.-English Ser. 38, 2187–2198 (2022). https://doi.org/10.1007/s10114-022-0581-0

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  • DOI: https://doi.org/10.1007/s10114-022-0581-0

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