On regularity criterion to the 3D axisymmetric incompressible MHD equations

This paper is concerned with the regularity criterion for a class of axisymmetric solutions to 3D incompressible magnetohydrodynamic equations. More precisely, for the solutions that have the form of u = u_re_r+u_θe_θ+u_ze_z and b = b_θe_θ, we prove that if |ru(x,t)|≤C holds for ?1≤t < 0, then (u,b) is regular at time zero. This result can be thought as a generalization of recent results in for the 3D incompressible Navier‐Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd.