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An improved regularity criterion of three-dimensional magnetohydrodynamic equations. (English) Zbl 1239.76070
Summary: An improved regularity criterion for a weak solution of three-dimensional magnetohydrodynamic equations is obtained. Employing the Fourier localization technique, it is proved that weak solutions become regular on (0,T] if the summation of velocity field u and magnetic field b belong to the largest critical spaces: u+bL 2 1+r (0,T;(B , r ( 3 )), -1<r1. This obviously extends the previous results.
MSC:
76W05Magnetohydrodynamics and electrohydrodynamics
35Q35PDEs in connection with fluid mechanics
76M25Other numerical methods (fluid mechanics)
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