WIAS Preprint No. 2663, (2019)

The sharp-interface limit for the Navier--Stokes--Korteweg equations


Authors

  • Abels, Helmut
    ORCID: 0000-0002-6606-4352
  • Daube, Johannes
  • Kraus, Christiane
  • Kröner, Dietmar

2010 Mathematics Subject Classification

  • 35B40 76T10 35Q35, 35R35

Keywords

  • Sharp-interface limit, diffuse-interface model, liquid-vapour flow, Navier--Stokes--Korteweg system, free-boundary problem.

DOI

10.20347/WIAS.PREPRINT.2663

Abstract

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.

Appeared in

  • C. Klingenberg, M. Westdickenberg (eds.), Theory, Numerics and Applications of Hyperbolic Problems I. HYP 2016. Springer Proceedings in Mathematics & Statistics. vol. 236, Springer, Cham.

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