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Partial regularity for the 3D magneto-hydrodynamics system with hyper-dissipation

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Abstract

We prove that for the 3D MHD equations with hyper-dissipations (-Δ)α (1 < α < 5/4) the Hausdorff dimension of singular set at the first blowing up time is at most 5 − 4α, by means of physical and frequency localization, Bony’s paraproduct and Littlewood-Paley theory.

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Correspondence to Wei Ren.

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The second author is supported by National Natural Science Foundation of China (Grant No. 11101405) and the President Fund of UCAS

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Ren, W., Wu, G. Partial regularity for the 3D magneto-hydrodynamics system with hyper-dissipation. Acta. Math. Sin.-English Ser. 31, 1097–1112 (2015). https://doi.org/10.1007/s10114-015-4498-8

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  • DOI: https://doi.org/10.1007/s10114-015-4498-8

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