Distributional equation in the limit of phase transition for fluids

We study the convergence of a diffusive interface model to a sharp interface model. The model consists of the conservation of mass and momentum, where the mass undergoes a phase transition. The equations were considered in [W3] and in the diffuse case consist of the compressible Navier– Stokes system coupled with an Allen–Cahn equation. In the sharp interface limit a jump in the mass density as well as in the velocity occurs. The convergence of mass and momentum is considered in the distributional sense. The convergence of the free energy to a limit is shown in a separate paper. The procedure in this paper works also in other general situations.