1 Admissible Phase Transitions

We are concerned with the structural stability of dynamic phase changes occurring across sharp interfaces in a multidimensional van der Waals uid. Such phase transitions can be viewed as propagating discontinuities. However, they are usually subsonic, thus violating the Lax criterion. The lacking information lies in an additional jump condition, which is rather simple in the case of reversible phase transitions. This enabled us, in a previous work, to prove the weak linearized stability of reversible planar phase boundaries. This stability has to be understood in the sense introduced by Majda for shock fronts. It means that a generalized Lopatinski condition is satissed. The aim of this paper is to point out the innuence of viscosity on the stability of phase transitions. More speciically, we use the nondimensional parameter measuring the competition between viscosity and capillarity, to work by perturbation. We show that this parameter being positive stabilizes the phase transitions. We thus nd that dissipative planar phase boundaries are uniformly linearly stable, in the sense of the uniform Lopatinski condition.