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 derivative(r)u(z), partial derivative(r)b(z), u(r), b(r), partial derivative(z)u(theta), partial derivative(z)b(theta); u(r), b(r), partial derivative(r)u(theta), partial derivative(r)b(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.

Automated summary

This study presents several weighted regularity criteria for axisymmetric solutions to the three-dimensional magnetohydrodynamic equations, which can effectively describe the relationships between velocity and vorticity components.