Nonlinear stability of axisymmetric ideal magnetohydrodynamic flows

In this paper the general theory developed by Vladimirov et al. is extended to nonlinear (Lyapunov) stability for axisymmetric (invariant under rotations around a fixed axis) solutions of the ideal incompressible magnetohydrodynamic flows for a particular situation, namely arbitrary field and poloidal flow. The appropriate norm is a sum of magnetic and kinetic energies and the mean square vector potential of the magnetic field.