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A remark on the Beale-Kato-Majda criterion for the 3D MHD equations with zero kinematic viscosity

A remark on the Beale-Kato-Majda criterion for the 3D MHD equations with zero kinematic viscosity In this paper, we study the blow-up criterion of smooth solutions to the 3D magneto-hydrodynamic system in $$\dot B_{\infty ,\infty }^0$$ . 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A remark on the Beale-Kato-Majda criterion for the 3D MHD equations with zero kinematic viscosity

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References (18)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-012-0140-z
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study the blow-up criterion of smooth solutions to the 3D magneto-hydrodynamic system in $$\dot B_{\infty ,\infty }^0$$ . 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.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Apr 29, 2012

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