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

Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data