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In this paper, we are concerned with the global well-posedness of atri-dimensional MHD system with only vertical viscosity in velocity equationfor the large axisymmetric initial data. By making good use of the axisymmetricstructure of flow and the maximal smoothing effect of vertical diffusion, weshow that $\displaystyle\sup_{2\leqp<\infty}\int_0^t\frac{\|\partial_{z}u(\tau)\|_{L^p}^{2}}{p^{3/4}}\,\mathrm{d}\tau<\infty$.With this regularity for the vertical first derivative of velocity vectorfield, we further establish losing estimates for the anisotropy tri-dimensionalMHD system to get the high regularity of $(u,b)$, which guarantees that$\int_0^t\|\nabla u(\tau)\|_{L^\infty}\,\mathrm{d}\tau<\infty$. This togetherwith the classical commutator estimate entails the global regularity of asmooth solution.

Global well-posedness for axisymmetric MHD system with only vertical viscosity