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Non blow-up criterion for the 3-D Magneto-hydrodynamics equations in the limiting case

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Abstract

In this paper, we prove that suitable weak solution (u, b) of the 3-D MHD equations can be extended beyond T if u ∈ L ∞(0, T;L 3(ℝ3)) and the horizontal components b h of the magnetic field satisfies the well-known Ladyzhenskaya–Prodi–Serrin condition, which improves the corresponding regularity criterion by Mahalov–Nicolaenko–Shilkin.

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Acknowledgements

We thank the referees for their time and comments. The author also would like to thank Prof. Zhifei Zhang for some helpful discussions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P. R. China

    Wen Dong Wang

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  1. Wen Dong Wang
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Correspondence to Wen Dong Wang.

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Supported by NSFC (Grant Nos. 11301048, 11671067), the Fundamental Research Funds for the Central Universities and the Institute of Mathematical Sciences of CUHK

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Wang, W.D. Non blow-up criterion for the 3-D Magneto-hydrodynamics equations in the limiting case. Acta. Math. Sin.-English Ser. 33, 969–980 (2017). https://doi.org/10.1007/s10114-017-6276-2

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  • DOI: https://doi.org/10.1007/s10114-017-6276-2

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