The magnetohydrodynamical system in bounded $\mathscr{C}^1$ domains of dimension $n\ge3$

Abstract: Existence of mild solutions for the magnetohydrodynamical system in $\mathscr{C}<sup>1$ domains is established in critical spaces in dimension $n\ge 3$. The proof relies on recent regularity results on the Stokes operator in $\mathscr{C}<sup>1$ domains and a Leibniz-like formula for differential forms proved here in Section 2.