We investigate the three-dimensional (3D) axially symmetric magnetohydrodynamic (MHD) boundary layer equations without structural assumptions. The initial data is small, belongs to the $H^{1}$ Sobolev space with respect to the normal variable, and is analytic with respect to the tangential variables. Under this condition, we establish the global well-posedness of the equations in an analytic space. Motivated by the approach in (Ignatova and Vicol in Arch. Ration. Mech. Anal. 220:809–848, 2016; Pan and Xu in Chin. Ann. Math., Ser. B 45(4):573–596, 2024), our proof hinges on constructing a tangentially weighted analytic energy functional, which acts on a specially designed “good unknown” to overcome the inherent challenges of the boundary layer system.
