  Existence of local-in-time unique solution and loss of smoothness of full
Magnet-Hydro-Dynamics system (MHD) is considered for periodic initial data. The
result is proven using Fujita-Kato's method in $\ell^1$ based (for the Fourier
coefficients) functional spaces enabling us to easily estimate nonlinear terms
in the system as well as solutions to Maxwells's equations. A loss of
smoothness result is shown for the velocity and magnetic field. It comes from
the damped-wave operator which does not have any smoothing effect.
