Abstract: We prove the incompressible limit of non-isentropic ideal MHD equations with a perfectly conducting boundary for general initial data. The key observation is based on a special structure in vorticity analysis which motivates us to establish uniform estimates in certain anisotropic Sobolev norms. This is based on a joint work with Prof. Qiangchang Ju and Dr. Jiawei Wang. Combining this with techniques in free-boundary problems, we prove the incompressible limit for current-vortex sheets with well-prepared initial data.
