Density Oscillations at the Interface Between Vapor and Liquid

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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 βc and a second critical value β*>βc, becoming oscillatory after β* and overshooting the equilibrium density of the liquid phase infinitely often.

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