Geodesic
Logarithmically improved blow-up criterion for smooth solutions to the Leray-$\alpha $-magnetohydrodynamic equations
Archivum mathematicum, Tome 55 (2019) no. 1, pp. 55-68.

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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.
DOI : 10.5817/AM2019-1-55
Classification : 35B40, 76D03
Keywords: magnetohydrodynamic-$\alpha $ model; regularity criterion; Besov space 
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     title = {Logarithmically improved blow-up criterion for smooth solutions to the {Leray-}$\alpha $-magnetohydrodynamic equations},
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Ben Omrane, Ines; Gala, Sadek; Kim, Jae-Myoung; Ragusa, Maria Alessandra. Logarithmically improved blow-up criterion for smooth solutions to the Leray-$\alpha $-magnetohydrodynamic equations. Archivum mathematicum, Tome 55 (2019) no. 1, pp. 55-68. doi : 10.5817/AM2019-1-55. http://geodesic.mathdoc.fr/articles/10.5817/AM2019-1-55/

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