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

  • Helmut Abels
  • Johannes Daube
  • Christiane Kraus
  • Dietmar Kröner
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 236)


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.


Sharp-interface limit Diffuse-interface model Liquid–vapour flow Navier–Stokes–Korteweg system Free-boundary problem 

MSC (2010)

35B40 76T10 35Q35 35R35 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  2. 2.Abteilung für Angewandte MathematikUniversität FreiburgFreiburgGermany
  3. 3.Weierstraß-InstitutBerlinGermany

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