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

  • Weihua WangEmail author


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 \(\alpha = 1\)).


Magnetohydrodynamics Fractional MHD Variable Fourier–Besov spaces Gevrey class 

Mathematics Subject Classification

Primary 42B37 76W05 46F30 Secondary 35S30 49N60 



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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesYangzhou UniversityYangzhouChina
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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