Address:
Sadek Gala, Department of Mathematics, ENS of Mostaganem Box 227, Mostaganem 27000, Algeria and Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria, 6 95125 Catania, Italy,
Maria Alessandra Ragusa, RUDN University, 6 Miklukho – Maklay St, Moscow, 117198, Russia, and Dipartimento di Matematica e Informatica, Università di Catania,
Jae-Myoung Kim, Department of Mathematical Sciences, Seoul National University, Seoul, Republic of Korea,
Ines Ben Omrane, Department of Mathematics, Faculty of Science, Al Imam Mohammad Ibn Saud, Islamic University (IMSIU), P. O. Box 90950, Riyadh 11623, Saudi Arabia
E-mail:
sgala793@gmail.com
maragusa@dmi.unict.it
cauchy02@naver.com
imbenomrane@imamu.edu.sa.
Abstract: 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.
AMSclassification: primary 35B40; secondary 76D03.
Keywords: magnetohydrodynamic-\alpha model, regularity criterion, Besov space.
DOI: 10.5817/AM2019-1-55