Logarithmically improved blow-up criterion for smooth solutions to the Leray- α -magnetohydrodynamic equations

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

Archivum Mathematicum (2019)

  • Volume: 055, Issue: 1, page 55-68
  • ISSN: 0044-8753

Abstract

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

How to cite

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Omrane, Ines Ben, et al. "Logarithmically improved blow-up criterion for smooth solutions to the Leray-$\alpha $-magnetohydrodynamic equations." Archivum Mathematicum 055.1 (2019): 55-68. <http://eudml.org/doc/294781>.

@article{Omrane2019,
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.},
author = {Omrane, Ines Ben, Gala, Sadek, Kim, Jae-Myoung, Ragusa, Maria Alessandra},
journal = {Archivum Mathematicum},
keywords = {magnetohydrodynamic-$\alpha $ model; regularity criterion; Besov space},
language = {eng},
number = {1},
pages = {55-68},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Logarithmically improved blow-up criterion for smooth solutions to the Leray-$\alpha $-magnetohydrodynamic equations},
url = {http://eudml.org/doc/294781},
volume = {055},
year = {2019},
}

TY - JOUR
AU - Omrane, Ines Ben
AU - Gala, Sadek
AU - Kim, Jae-Myoung
AU - Ragusa, Maria Alessandra
TI - Logarithmically improved blow-up criterion for smooth solutions to the Leray-$\alpha $-magnetohydrodynamic equations
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 1
SP - 55
EP - 68
AB - 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.
LA - eng
KW - magnetohydrodynamic-$\alpha $ model; regularity criterion; Besov space
UR - http://eudml.org/doc/294781
ER -

References

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