Abstract

In this paper we obtain a new regularity criterion for weak solutions to the 3D MHD equations. It is proved that if $\mathrm{div}( \frac{u}{|u|}) $ belongs to $L^{\frac{2}{1-r}}( 0,T;\dot{X}_{r}( \mathbb{R}^{3}) ) $ with 0?r?1, then the weak solution actually is regular and unique.

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