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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 $\left(0,T\right]$ if the summation of velocity field $u$ and magnetic field $b$ belong to the largest critical spaces: $u+b\in {L}^{\frac{2}{1+r}}\left(0,T;\left({B}_{\infty ,\infty }^{r}\left({ℝ}^{3}\right)\right)$, $-1. This obviously extends the previous results.
##### MSC:
 76W05 Magnetohydrodynamics and electrohydrodynamics 35Q35 PDEs in connection with fluid mechanics 76M25 Other numerical methods (fluid mechanics)
##### Keywords:
MHD equations; regularity criterion; Besov space
##### References:
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