The Beale-Kato-Majda Criterion for the 3D Magneto-Hydrodynamics Equations |
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| Authors: | Qionglei Chen Changxing Miao Zhifei Zhang |
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| Affiliation: | (1) Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, P. R. China;(2) School of Mathematical Science, Peking University, Beijing, 100871, P. R. China |
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| Abstract: | We study the blow-up criterion of smooth solutions to the 3D MHD equations. By means of the Littlewood-Paley decomposition, we prove a Beale-Kato-Majda type blow-up criterion of smooth solutions via the vorticity of velocity only, namely where Δ j is the frequency localization operator in the Littlewood-Paley decomposition. |
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