WIAS Preprint No. 1545, (2010)

Asymptotic analysis for Korteweg models



Authors

  • Dreyer, Wolfgang
  • Giesselmann, Jan
  • Kraus, Christiane
  • Rohde, Christian

2010 Mathematics Subject Classification

  • 76T10 35C20 35R35

Keywords

  • Liquid vapor flow, phase transition, asymptotic analysis, sharp interface limit

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.

Appeared in

  • Interfaces Free Bound., 14 (2012) pp. 105--143.

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