Regularity criteria to the axisymmetric incompressible Magneto-hydrodynamics equations

In this paper, we investigate the regularity criteria of axisymmetric solutions to the incompressible MHD equations, which have the form u = u(r)e(r) + u(theta)e(theta). + u(z)e(z) and b = b(theta)e(theta). Through establishing some innovative estimates, we obtain some new regularity criteria that are scaling invariant and independent of b(theta). To some extent, our work can be seen as a generation of the result by D. Chae and J. Lee [9] on the axisymmetric incompressible Navier-Stokes equations.