Geodesic
Interface conditions for limits of the Navier–Stokes–Korteweg model
Katharina Hermsdörfer1 ; Christiane Kraus2 ; Dietmar Kröner1
1Universität Freiburg, Germany
2Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
Interfaces and free boundaries, Tome 13 (2011) no. 2, pp. 239-254

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We study the behaviour of the pressure across phase boundaries in liquid-vapour flows. As mathematical model, we 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 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 situations.
DOI : 10.4171/ifb/256
Classification : 76-XX, 35-XX, 82-XX, 00-XX
Mots-clés : liquid-vapour flows; van der Waals–Cahn–Hilliard energy; Navier–Stokes–Korteweg system; singular perturbations

Katharina Hermsdörfer  1   ; Christiane Kraus  2   ; Dietmar Kröner  1

1 Universität Freiburg, Germany
2 Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany 
Katharina Hermsdörfer; Christiane Kraus; Dietmar Kröner. Interface conditions for limits of the Navier–Stokes–Korteweg model. Interfaces and free boundaries, Tome 13 (2011) no. 2, pp. 239-254. doi: 10.4171/ifb/256
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     author = {Katharina Hermsd\"orfer and Christiane Kraus and Dietmar Kr\"oner},
     title = {Interface conditions for limits of the {Navier{\textendash}Stokes{\textendash}Korteweg} model},
     journal = {Interfaces and free boundaries},
     pages = {239--254},
     year = {2011},
     volume = {13},
     number = {2},
     doi = {10.4171/ifb/256},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/256/}
}
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