In this talk we study the stability of multidimensional contact dis-continuities in compressible °uids. There are two kinds of contact dis-continuities, one is so-called the vortex sheet, mainly due to that the tangential velocity is discontinuous across the front, and the other one is the entropy wave, for which the velocity is continuous while the entropy has certain jump on the front.

It is well-known that the vortex sheet in two dimensional compress-ipble Euler equations is stable when the Mach number is larger than 2, while in three dimensional problem it is always unstable. But, some physical phenomena indicate that the magnetic ¯eld has certain stabilization e®ect for waves in °uids. The ¯rst goal of this talk is to rig-orously justify this physical phenomenon, and to investigate the stabil-ity of three-dimensional current-vortex sheet in compressible magneto-hydrodynamics. By using energy method and the Nash-Moser iteration scheme, we obtain that the current-vortex sheet in three-dimensional compressible MHD is linearly and nonlinearly stable when the magnetic ¯elds on both sides of the front are non-parallel to each other. The second goal is to study the stability of entropy waves. By a

simple computation, one can easily observe that the entropy wave is structurally unstable in gas dynamics. By carefully studying the e®ect of magnetic ¯elds on entropy waves, we obtain that the entropy wave in three-dimensional compressible MHD is stable when the normal mag-netic ¯eld is continuous and non-zero on the front.