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The purpose of this paper is to study the incompressible non-resistive MHDequations in $\mathbb{R}^3$. We establish the global well-posedness ofclassical solutions if the initial data is axially symmetric and the swirlcomponents of the velocity and magnetic vorticity vanish. In particular, thespecial axially symmetric initial data can be arbitrarily large and satisfy lowregularity assumptions.

Global smooth solutions to the 3D non-resistive MHD equations with low regularity axisymmetric data