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Partial regularity for the 3D magneto-hydrodynamics system with hyper-dissipation |
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| Authors: | Wei Ren Gang Wu |
| Institution: | 1. Department of Mathematics and Systems Science, BeiHang University, Beijing 100191, P. R. China; 2. School of Mathematical Science, University of Chinese Academy of Science, Beijing 100049, P. R. China |
| 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. |
| Keywords: | 3D MHD system fractal dissipation partial regularity physical and frequency localization Bony's paraproduct decomposition |
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