On the stability of Alfven discontinuity

The stability of Alfvén discontinuities for the equations of ideal compressible magneto-hydrodynamics (MHD) is studied. The Alfvén discontinuity is a characteristic discontinuity for the hyperbolic system of MHD equations but, as in the case of shock waves, there is a mass flux through its front. The Lopatinskii condition for a planar Alfvén discontinuity is tested numerically, and the domain in the space of parameters of the discontinuity where it is unstable is determined. In fact, in this domain the Alfvén discontinuity is not only unstable, but the initial-boundary-value problem for corresponding linearized equations is ill-posed in the sense of Hadamard.