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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.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Apr 29, 2012
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