Methods and Applications of Analysis

Volume 20 (2013)

Number 2

A free boundary model for Korteweg fluids as a limit of barotropic compressible Navier-Stokes equations

Pages: 165 – 178

DOI: https://dx.doi.org/10.4310/MAA.2013.v20.n2.a4

Authors

Stéphane Labbé (Laboratoire Jean Kuntzmann, Grenoble University, and CNRS, Grenoble, France)

Emmanuel Maitre (Laboratoire Jean Kuntzmann, Grenoble University, and CNRS, Grenoble, France)

Abstract

We consider the limit of some barotropic compressible fluid model with Korteweg forcing term, studied in [1], as the exponent of the barotropic law goes to infinity. This provides a free boundary problem model, with capillary effects, and therefore generalizes the free boundary model obtained by Lions and Masmoudi [5]. Our interest for such free boundary problem stems from a study of the Leidenfrost effect.

Keywords

compressible Navier-Stokes equations, Korteweg fluid, free boundary problem

2010 Mathematics Subject Classification

35Q30, 35R35, 76N10, 76T10

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Published 25 September 2013