  We study the local and global wellposedness of a full system of
Magneto-Hydro-Dynamic equations. The system is a coupling of the forced
(Lorentz force) incompressible Navier-Stokes equations with the Maxwell
equations through Ohm's law for the current. We show the local existence of
mild solutions for arbitrarily large data in a space similar to the scale
invariant spaces classically used for Navier-Stokes. These solutions are global
if the initial data are small enough.
