Free boundary problem of low Mach number magnetohydrodynamic flows

In this paper we consider a free boundary problem of low Mach number magnetohydrodynamic flow in spatial dimension n $\ge$ 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].