A remark on the Beale-Kato-Majda criterion for the 3D MHD equations with zero kinematic viscosity |
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| Authors: | Sadek Gala Xiao-chun Chen |
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| Institution: | 1 Department of Mathematics,University of Mostaganem,Box 227,Mostaganem 27000,Algeria2 Department of Mathematics,Chonqing Three Gorges University,Wanzhou 404000,China |
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| Abstract: | In this paper, we study the blow-up criterion of smooth solutions to the 3D magneto-hydrodynamic system in (B)\dot]￥,￥0\dot B_{\infty ,\infty }^0. We show that a smooth solution of the 3D MHD equations with zero kinematic viscosity in the whole space R3 breaks down if
and only if certain norm of the vorticity blows up at the same time. |
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| Keywords: | Magneto-hydrodynamic equations with zero viscosity ˙ B 0 ∞ ∞ space blow-up criterion 2000 MR Subject Classification 35Q35 35B65 76D05 |
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