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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: \(u+b\in L^{\frac{2}{1+r}}(0,T;(B^r_{\infty, \infty}(\mathbb{R}^3))\), \(-1<r\leq 1\). This obviously extends the previous results.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
35Q35 PDEs in connection with fluid mechanics
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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