Global well-posedness for axisymmetric MHD equations with vertical dissipation and vertical magnetic diffusion

In this paper, the unique global strong axisymmetric solutions for the incompressible MHD equations with only vertical dissipation and vertical magnetic diffusion are established, where no smallness assumptions on the initial data are required. One of the key ingredients of the analysis is to obtain higher-order regularity estimates for velocity and magnetic fields, where the axisymmetry of the solutions and some new L (2) energy estimates play an important role.