JournalsifbVol. 14, No. 1pp. 105–143

Asymptotic analysis for Korteweg models

  • Wolfgang Dreyer

    Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
  • Jan Giesselmann

    Universität Stuttgart, Germany
  • Christiane Kraus

    Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
  • Christian Rohde

    Universität Stuttgart, Germany
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Abstract

This paper deals with a sharp interface limit of the isothermal Navier–Stokes–Korteweg system. The sharp interface limit is performed by matched asymptotic expansions of the fields in powers of the interface width ". These expansions are considered in the interfacial region (inner expansions) and in the bulk (outer expansion) and are matched order by order. Particularly we consider the first orders of the corresponding inner equations obtained by a change of coordinates in an interfacial layer. For a specific scaling we establish solvability criteria for these inner equations and recover the results within the general setting of jump conditions for sharp interface models.

Cite this article

Wolfgang Dreyer, Jan Giesselmann, Christiane Kraus, Christian Rohde, Asymptotic analysis for Korteweg models. Interfaces Free Bound. 14 (2012), no. 1, pp. 105–143

DOI 10.4171/IFB/275