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Zbl 1239.76070
Dong, Bo-Qing; Jia, Yan; Zhang, Wenliang
An improved regularity criterion of three-dimensional magnetohydrodynamic equations.
(English)
[J] Nonlinear Anal., Real World Appl. 13, No. 3, 1159-1169 (2012). ISSN 1468-1218

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: $u+b\in L^{\frac{2}{1+r}}(0,T;(B^r_{\infty, \infty}(\bbfR^3))$, $-1<r\le 1$. This obviously extends the previous results.
MSC 2000:
*76W05 Flows in presence of electromagnetic forces
35Q35 Other equations arising in fluid mechanics
76M25 Other numerical methods

Keywords: MHD equations; regularity criterion; Besov space

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