Remarks on the regularity criteria for the axisymmetric MHD system

We show several weighted regularity criteria for the axisymmetric solutions to the three-dimensional magnetohydrodynamic equations, involving $u^r, u^z$; $u^r, b^r, \partial _ru^z, \partial _rb^z$; $u^r,b^r, \partial _zu^\theta , \partial _zb^\theta $; $u^r, b^r, \partial _ru^\theta , \partial _rb^\theta $; or $\omega ^\theta $, where $u^r,u^\theta ,u^z$ are the angular, swirl and axial components of the velocity respectively and $\omega ^\theta $ denotes the swirl component of the vorticity.