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Keywords:
magnetohydrodynamic-$\alpha $ model; regularity criterion; Besov space
magnetohydrodynamic-$\alpha $ model; regularity criterion; Besov space
Summary:
In this paper, the Cauchy problem for the $3D$ Leray-$\alpha $-MHD model is investigated. We obtain the logarithmically improved blow-up criterion of smooth solutions for the Leray-$\alpha $-MHD model in terms of the magnetic field $B$ only in the framework of homogeneous Besov space with negative index.
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