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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References:

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