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The current paper establishes the global well-posedness issue for the fullviscous MHD equations in the axisymmetric setting. Global solutions areobtained in critical Besov spaces uniformly to the viscosity when theresistivity is fixed in the spirit of \cite{AKH,Hassainia,hz0}. Furthermore,strong convergence in the resolution spaces with a rate of convergence is alsostudied.

On the vanishing viscosity limit for the full viscous MHD system with critical axisymmetric initial data