  We give a description of a magnetohydrodynamical system in $n$ dimension
using the exterior derivative. We then prove existence of global solutions for
small initial data and local existence for arbitrary large data in two classes
of critical spaces -- $L^q_tL^p_x$ and $\mathcal{C}_tL^p_x$, as well as
uniqueness for solutions in $\mathcal{C}_tL^p_x$.
