Density Oscillations at the Interface Between Vapor and Liquid

We study the interface between liquid and vapor in the context of the van der Waals theory, considering the non-local free energy functional recently derived by Lebowitz, Mazel, and Presutti from a system of particles in the continuum with Kac potentials. We prove that the density profile between vapor and liquid is monotone when the inverse temperature is between the critical value _c and a second critical value *> _c , becoming oscillatory after * and overshooting the equilibrium density of the liquid phase infinitely often.