Existence and uniqueness in critical spaces for the magnetohydrodynamical system in $\mathbb{R}^n$

Abstract

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 $\mathcal{C}_tL^p_x$.