On the Incompressible Limit of Current-Vortex Sheets with or without Surface Tension
arxiv(2024)
摘要
This is the second part of the two-paper sequence, which aims to present a
comprehensive study for compressible current-vortex sheets with or without
surface tension in ideal compressible magnetohydrodynamics (MHD). The results
of this paper are two-fold: First, we establish the zero-surface-tension limit
of compressible current-vortex sheets under certain stability conditions on the
free interface; Second, when the two-phase flows are isentropic and the density
functions converge to the same constant as Mach number goes to zero, we can
drop the boundedness assumption (with respect to Mach number) on high-order
time derivatives by combining the paradifferential approach applied to the
evolution equation of the free interface, the structure of wave equations for
the total pressure and the anisotropic Sobolev spaces with suitable weights of
Mach number. To our knowledge, this is the first result that rigorously
justifies the incompressible limit for both compressible vortex sheets and
free-surface ideal MHD flows.
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