A theorem of existence for the equations of magnetohydrodynamics of partially ionized plasmas

The equations of magnetohydrodynamics of partially ionized plasmas have been known for a long time, but rarely studied. Instead, several simplifications have been applied to different physical models, ranging from magnetic reconnection to ambipolar drift. The original system relates the electric field to kinetic magnitudes by means of a non-local law, so that the equations describing it involve partial differentials as well as functional operators. We prove a theorem of existence and uniqueness of solutions for a finite time by means of a fixed point argument in an appropriate functional setting.