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 beta(c) and a second critical value beta*>beta(c), becoming oscillatory after beta* and overshooting the equilibrium density of the liquid phase infinitely often