Global Well-Posedness of 3D Axisymmetric MHD System with Pure Swirl Magnetic Field

In this paper, we consider the axisymmetric MHD system with nearly critical initial data having the special structure: \(u_{0}=u_{0}^{r} e_{r}+u^{\theta}_{0} e_{\theta}+u_{0}^{z} e_{z}\), \(b_{0}=b_{0}^{\theta}e_{\theta}\). We prove that, this system is globally well-posed provided the scaling-invariant norms \(\|ru^{\theta}_{0}\|_{L^{\infty}}\), \(\|r^{-1}b^{\theta}_{0}\| _{L^{\frac{3}{2}}}\) are sufficiently small.