TY - JOUR

T1 - Regularity criteria of MHD system involving one velocity and one current density component

AU - Yamazaki, Kazuo

PY - 2014/9

Y1 - 2014/9

N2 - We study a regularity criteria of the three-dimensional magnetohydrodynamics system. In particular, we obtain a regularity criteria that involves one velocity component and one current density component. Its immediate consequence is a regularity criteria in terms of one velocity component and two entries from the Jacobian matrix of the magnetic vector field, in contrast to many previous results that involve three entries all from the Jacobian matrix of the velocity vector field. Moreover, the conditions on the current density component is in the norm with scaling dimension zero; i.e. Serrin-class.

AB - We study a regularity criteria of the three-dimensional magnetohydrodynamics system. In particular, we obtain a regularity criteria that involves one velocity component and one current density component. Its immediate consequence is a regularity criteria in terms of one velocity component and two entries from the Jacobian matrix of the magnetic vector field, in contrast to many previous results that involve three entries all from the Jacobian matrix of the velocity vector field. Moreover, the conditions on the current density component is in the norm with scaling dimension zero; i.e. Serrin-class.

KW - Magnetohydrodynamics system

KW - Navier-Stokes equations

KW - Regularity criteria.

UR - http://www.scopus.com/inward/record.url?scp=84906829331&partnerID=8YFLogxK

U2 - 10.1007/s00021-014-0178-1

DO - 10.1007/s00021-014-0178-1

M3 - Article

AN - SCOPUS:84906829331

VL - 16

SP - 551

EP - 570

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

SN - 1422-6928

IS - 3

ER -