Refined blow-up criterion for the 3D magnetohydrodynamics equations

Abstract

In this paper, we prove a refined blow-up criterion for the 3D magnetohydrodynamics equations. With the help of the Littlewood–Paley decomposition, we show an Osgood type blow-up criterion in term of

where denotes the Fourier localization operator and

Keywords:

• blow-up criterion
• MHD equations
• Besov spaces

AMS Subject Classifications:

• 76W05
• 35B65

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Erratum

Acknowledgements

The author would like to thank Professor J. Fan for proposing the problem. The author was partly supported by the NSF of China (No. 11171034). The author was also supported by the Innovation Foundation of BUAA for Ph.D. graduates.