  We examine hyperbolicity of general relativistic magnetohydrodynamics with
divergence cleaning, a flux-balance law form of the model not covered by our
earlier analysis. The calculations rely again on a dual-frame approach, which
allows us to effectively exploit the structure present in the principal part.
We find, in contrast to the standard flux-balance law form of the equations,
that this formulation is strongly hyperbolic, and thus admits a well-posed
initial value problem. Formulations involving the vector potential as an
evolved quantity are then considered. Carefully reducing to first order, we
find that such formulations can also be made strongly hyperbolic. Despite the
unwieldy form of the characteristic variables we therefore conclude that of the
free-evolution formulations of general relativistic magnetohydrodynamics
presently used in numerical relativity, the divergence cleaning and vector
potential formulations are preferred.
