The current paper aims to explore the three-dimensional axisymmetric viscous and resistive magnetohydrodynamic system. This article is concerned with two outcomes, in the first result we prove the global existence of a unique solution for this system under initial data lying in the Sobolev spaces Hs × Hs−2 with s>52, furthermore, we obtain uniform estimates with respect to the viscosity. The second outcome shows that the viscous and resistive solutions (vμ,bμ)μ>0 strongly converge to the non-viscous one (v, b). This convergence is performed in the space L(R+,Hs2×Hs2), also we obtain that the rate of convergence is (μt).

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