题目：Structural stability and incompressible limit of current-vortex sheets in ideal compressible MHD
摘要：The current-vortex sheet, as one of the characteristic contact discontinuities in ideal compressible MHD, is described by a free-interface problem for two-phase MHD flows with tangential magnetic fields on the interface. We prove local well-posedness, nonlinear stability and incompressible limit for current-vortex sheets with or without surface tension within one attempt. One of the key observations is a hidden structure of Lorentz force in vorticity analysis which motivates us to use certain anisotropic Sobolev spaces instead of standard Sobolev spaces. Our result demonstrates that either suitable magnetic fields or surface tension could suppress the analogue of Kelvin-Helmholtz instability for compressible vortex sheets. To our knowledge, this is the first result that rigorously justifies the incompressible limit of vortex sheets.