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Isaac Newton Institute for Mathematical Sciences

Sharp interface limit for the Navier-Stokes-Korteweg model

Presenter: Johannes Daube (University of Freiburg)

Co-authors: Helmut Abels (University of Freiburg), Christiane Kraus (WIAS Berlin), Dietmar Kröner (University of Freiburg)


The Navier-Stokes-Korteweg model, an extension of the compressible Navier-Stokes equations, is a diffuse interface model for liquid-vapour flows which allows for phase transitions \cite{korteweg}. In the model, a small parameter $\varepsilon >0$ represents the thickness of an interfacial area, where phase transitions occur. Its static version was studied by Hermsdörfer, Kraus and Kröner and the corresponding interface conditions were obtained. Assuming convergence of an associated energy functional to a suitable surface measure, we will perform the sharp interface limit for $\varepsilon \rightarrow 0$ in the dynamic case. More precisely, by means of compactness, we will ensure that solutions to the diffusive Navier-Stokes-Korteweg equations converge to solutions of an appropriate sharp interface model as $\varepsilon \rightarrow 0$. This is joint work with Helmut Abels (Regensburg), Christiane Kraus (Berlin) and Dietmar Kröner (Freiburg).