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Global well-posedness of the generalized magnetohydrodynamic equations

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Abstract

In this paper, we establish the global existence of mild solutions to the n-dimensional generalized MHD system provided that the norms of the initial data are bounded exactly by the minimal value of the viscosity coefficients and the fractional powers. In addition, we also establish the existence of the global small solution in the Fourier–Herz spaces. Finally, we prove the long time decay of the global solutions in the corresponding spaces.

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Acknowledgements

The authors would like to thank the anonymous referee and the associated editor for their constructive comments and helpful suggestions, which improve the presentation of this paper. Ye was supported by the National Natural Science Foundation of China (No. 11701232) and the Natural Science Foundation of Jiangsu Province (No. BK20170224).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Jiangsu Normal University, 101 Shanghai Road, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Zhuan Ye

  2. School of Science, Jiangnan University, 1800 Lihu Road, Wuxi, 214122, People’s Republic of China

    Xiaopeng Zhao

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  1. Zhuan Ye
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  2. Xiaopeng Zhao
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Correspondence to Zhuan Ye.

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Ye, Z., Zhao, X. Global well-posedness of the generalized magnetohydrodynamic equations. Z. Angew. Math. Phys. 69, 126 (2018). https://doi.org/10.1007/s00033-018-1021-y

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  • DOI: https://doi.org/10.1007/s00033-018-1021-y

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