Free boundary problem of low Mach number magnetohydrodynamic flows

TL;DR

This paper investigates a free boundary problem in low Mach number magnetohydrodynamic flows, establishing a priori estimates and a blow-up criterion using geometric and analytical methods.

Contribution

It introduces a geometric approach to analyze the free boundary problem and derives new a priori estimates and blow-up criteria for low Mach number MHD flows.

Findings

A priori estimates of flow quantities in Sobolev norms

A blow-up criterion for the flow

Application of geometric methods to free boundary problems

Abstract

In this paper we consider a free boundary problem of low Mach number magnetohydrodynamic flow in spatial dimension n $\geq$ 2. A priori estimates of the second fundamental form and various flow quantities in Sobolev norms are obtained by adopting the geometrical point of view introduced by Christodoulou and Lindblad [3]. Moreover, a blow up criterion is derived by using the method of Beale, Kato and Majda [2].