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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Chen, X., Gala, S. & Guo, Z. A New Regularity Criterion in Terms of the Direction of the Velocity for the MHD Equations. Acta Appl Math 113, 207–213 (2011). https://doi.org/10.1007/s10440-010-9594-2
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DOI: https://doi.org/10.1007/s10440-010-9594-2