The magnetohydrodynamical system in bounded non smooth domains of dimension $n\ge3$

TL;DR

This paper proves the existence of mild solutions for the magnetohydrodynamical system in bounded C 1 domains of dimension n ≥ 3, utilizing recent regularity results and a new Leibniz-like formula for differential forms.

Contribution

It introduces new regularity results for the Stokes operator in C 1 domains and a Leibniz-like formula for differential forms, advancing the analysis of magnetohydrodynamical systems.

Findings

Existence of mild solutions in critical spaces for n ≥ 3

Regularity results for the Stokes operator in C 1 domains

A new Leibniz-like formula for differential forms

Abstract

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