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)er + u(0)(theta)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 parallel to ru(0)(theta)parallel to L infinity,parallel to r(-1)b(0)(theta)parallel to(3/2)(L), are sufficiently small.