WIAS Preprints

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Pressure reconstruction for weak solutions of the two-phase incompressible Navier--Stokes equations with surface tension
(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Abels, Helmut; Daube, Johannes; Kraus, Christiane
For the two-phase incompressible Navier--Stokes equations with surface tension, we derive an appropriate weak formulation incorporating a variational formulation using divergence-free test functions. We prove a consistency result to justify our definition and, under reasonable regularity assumptions, we reconstruct the pressure function from the weak formulation.
The 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, Dietmar
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.