Partial Regularity for the 3D Magneto-hydrodynamics System with Hyper-dissipation

We prove that for the 3D MHD equations with hyper-dissipations （-△）^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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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2015-07, Vol.31 (7), p.1097-1112
Main Authors: Ren, Wei, Wu, Gang
Format: Article
Language:English
Subjects:
Blowing time
Estimates
Fluid mechanics
Fourier transforms
Fractals
Frequencies
Hausdorff
Inequality
Localization
Magnetohydrodynamics
Mathematical analysis
Mathematics
Mathematics and Statistics
MHD
MHD方程
Navier-Stokes equations
Position (location)
Regularity
Spacetime
Studies
Three dimensional
三维
动力学系统
时间
消散
磁流体
耗散
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Summary:We prove that for the 3D MHD equations with hyper-dissipations （-△）^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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-015-4498-8