Well-Posedness in Gevrey Function Space for the 3D Axially Symmetric MHD Boundary Layer Equations Without Structural Assumption

In this paper, we establish the well-posedness theory for the three-dimensional axially symmetric magnetohydrodynamic (MHD) boundary layer system in Gevrey function space without any structural assumption. By using a refined cancellation mechanism to overcome the loss of tangential derivatives in the system and constructing a refined energy functional involves in a polynomial weight on the tangential variables to overcome the order mismatch between the tangentially radial field and the normal field, we show that the three-dimensional axially symmetric MHD boundary layer system is well-posed with Gevrey index up to 3/2. Our result is an extension of the previous work (Li and Yang in SIAM J Math Anal 53(3):3236–3264, 2021) from the MHD boundary layer system in both two- and three-dimensional spaces to the axisymmetric case.