Stability of subsonic planar phase boundaries in a van der Waals fluid

We are concerned with the structural stability of dynamic phase changes occ urring across sharp interfaces in a multidimensional van der Waals fluid. S uch phase transitions can be viewed as propagating discontinuities. However , they are usually subsonic, and thus undercompressive. The lacking informa tion lies in an additional jump condition, which may be derived from the vi scosity-capillarity criterion. This condition is rather simple in the case of reversible phase transitions, since it reduces to a generalized equal ar ea rule. In a previous work, I proved that reversible planar phase boundari es are weakly linearly stable, in the sense introduced by MAJDA for shock f ronts. This means that they satisfy a generalized Lopatinsky condition but not a uniform one. The aim of this paper is to point out the influence of v iscosity on the stability analysis, in order to deal with the more realisti c case of dissipative phase transitions. The main difficulty lies in the ad ditional jump condition, which is no longer explicit and depends on the (un known) internal structure of the interface. We overcome it by using bifurca tion arguments on the nondimensional parameter measuring the competition be tween viscosity and capillarity. We show by perturbation that the positivit y of this parameter stabilizes the phase transitions. As a conclusion, we f ind that dissipative planar phase boundaries are uniformly linearly stable, in the sense of the uniform Lopatinsky condition.