Logarithmically improved blow-up criterion for smooth solutions to the Leray-$\alpha $-magnetohydrodynamic equations

Ben Omrane, Ines   ; Gala, Sadek   ; Kim, Jae-Myoung   ; Ragusa, Maria Alessandra

Archivum mathematicum, Tome 55 (2019) no. 1, pp. 55-68

Abstract (VO)

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.

Détail

DOI : 10.5817/AM2019-1-55

Classification : 35B40, 76D03
Keywords: magnetohydrodynamic-$\alpha $ model; regularity criterion; Besov space

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