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 -- $L_t^q{L}_x^p$ and ${\mathcal{C}}_t{L}_x^p$, as well as uniqueness for solutions in ${\mathcal{C}}_t{L}_x^p$.

arXiv admin note: text overlap with arXiv:2103.03555 by other authors