The Sharp-Interface Limit for the Navier–Stokes–Korteweg Equations

We investigate the sharp-interface limit for the Navier–Stokes–Korteweg model, which is an extension of the compressible Navier–Stokes equations. By means of compactness arguments, we show that solutions of the Navier–Stokes–Korteweg equations converge to solutions of a physically meaningful free-boundary problem. Assuming that an associated energy functional converges in a suitable sense, we obtain the sharp-interface limit at the level of weak solutions.