A New Regularity Criterion in Terms of the Direction of the Velocity for the MHD Equations

Author： Chen Xiaochun  

Publisher： Springer Publishing Company

ISSN： 0167-8019

Source： Acta Applicandae Mathematicae, Vol.113, Iss.2, 2011-02, pp. : 207-213

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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|}) $</equationsource> belongs to $L^{\frac{2}{1-r}}( 0,T;\dot{X}_{r}( \mathbb{R}^{3}) ) $</equationsource> with 0≤r</i>≤1, then the weak solution actually is regular and unique.

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