Multi-dimensional stability of propagating phase boundaries

The paper addresses the multi-dimensional stability of propagating phase boundaries in real fluids, from a viewpoint similar to Majda's concerning classical discontinuities. For planar boundaries, a Lopatinski condition is derived and shown to be satisfied in the inviscid case. Some surface waves prevent the uniform Lopatinski condition to be satisfied though. Then it is shown that, for weakly dissipative phase boundaries, the surface waves are stabilized and the uniform Lopatinsky condition is satisfied.