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- ItemThe sharp-interface limit for the Navier--Stokes--Korteweg equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Abels, Helmut; Daube, Johannes; Kraus, Christiane; Kröner, DietmarWe 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.
- ItemInterface conditions for limits of the Navier-Stokes-Korteweg model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Hermsdörfer, Katharina; Kraus, Christiane; Kröner, DietmarIn this contribution we will study the behaviour of the pressure across phase boundaries in liquid-vapour flows. As mathematical model we will consider the static version of the Navier-Stokes-Korteweg model which belongs to the class of diffuse interface models. From this static equation a formula for the pressure jump across the phase interface can be derived. If we perform then the sharp interface limit we see that the resulting interface condition for the pressure seems to be inconsistent with classical results of hydrodynamics. Therefore we will present two approaches to recover the results of hydrodynamics in the sharp interface limit at least for special situ