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Global well-posedness of the MHD equations via the comparison principle

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Abstract

In this paper, we prove the global well-posedness of the incompressible magneto-hydrodynamics (MHD) equations near a homogeneous equilibrium in the domain \(\mathbb{R}^k\times\mathbb{T}^{d-k},d\geqslant2,k\geqslant1\) by using the comparison principle and constructing the comparison function.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11425103).

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Dongyi Wei & Zhifei Zhang

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  1. Dongyi Wei
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  2. Zhifei Zhang
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Correspondence to Zhifei Zhang.

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Wei, D., Zhang, Z. Global well-posedness of the MHD equations via the comparison principle. Sci. China Math. 61, 2111–2120 (2018). https://doi.org/10.1007/s11425-017-9217-8

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  • DOI: https://doi.org/10.1007/s11425-017-9217-8

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