The stability of current vortex sheets with transverse magnetic field

Abstract

Compared to the results in \cite{Shivamoggi}, using the normal mode method, we have rigorously confirmed that a transverse magnetic field reduces the stability of the system. Specifically, a larger velocity is required for stability in the presence of a magnetic field than in its absence. More precisely, when the magnitude of the magneto-acoustic Mach number $M_B:=\frac{{\dot{v}}_1^{+}}{{\bar{C}}_B}>\sqrt{2}$, we proved the well-posedness of the current vortex sheet problem for compressible MHD flows with a transverse magnetic field.