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Global well-posedness and analyticity for the 3D fractional magnetohydrodynamics equations in variable Fourier–Besov spaces

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Abstract

In this paper, we obtain the global well-posedness and analyticity of the 3D fractional magnetohydrodynamics equations in the critical variable Fourier–Besov spaces, which can be seen as a meaningful complement to the corresponding results of the magnetohydrodynamics equations in usual Fourier–Besov spaces. Moreover, our results are also new for the MHD equations (i.e., in the case of the classical dissipation \(\alpha = 1\)).

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Acknowledgements

The author wishes to express his thanks to Professor Ping Zhang from the Academy of Mathematics and Systems Science in Chinese Academy of Sciences for giving a guide to mathematical fluid mechanics. And the author would like to express his gratitude to the anonymous referees for their careful reading of the paper and valuable suggestions.

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  1. School of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, China

    Weihua Wang

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

    Weihua Wang

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 11771423, 11871452), the NSFC of Fujian (Grant Nos. 2017J01564, 2017J01563), and the National Science Foundation of Jiangsu Higher Education Institutions of China (Grant No. 19KJD100007)

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Wang, W. Global well-posedness and analyticity for the 3D fractional magnetohydrodynamics equations in variable Fourier–Besov spaces. Z. Angew. Math. Phys. 70, 163 (2019). https://doi.org/10.1007/s00033-019-1210-3

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