On the stability of Alfven discontinuity

The stability of Alfven discontinuities for the equations of ideal compressible magneto-hydrodynamics (MHD) is studied. The Alfven 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 Alfven 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 Alfven discontinuity is not only unstable, but the initial-boundary-value problem for corresponding linearized equations is ill-posed in the sense of Hadamard