Existence in critical spaces for the magnetohydrodynamical system in 3D bounded Lipschitz domains

TL;DR

This paper proves the existence of mild solutions for the 3D magnetohydrodynamical system within bounded Lipschitz domains, using critical space analysis and absolute boundary conditions.

Contribution

It introduces a novel approach to establish solution existence in critical spaces for the 3D MHD system with Lipschitz domain boundaries.

Findings

Existence of mild solutions in critical spaces

Solutions satisfy absolute boundary conditions

Applicable to bounded Lipschitz domains

Abstract

Existence of mild solutions for the 3D MHD system in bounded Lipschitz domains is established in critical spaces with the absolute boundary conditions.