Diffuse planar phase boundaries in a two-phase fluid with one incompressible phase
2013, Freistühler, Heinrich, Kotschote, Matthias
This note studies a family of Navier-Stokes-Allen-Cahn systems parameterized by temperature. Derived from an internal energy that corresponds to one incompressible and one compressible phase, this family is considered as a simple model for water. Decreasing temperature across a critical value, a transition takes places from a situation without towards one with planar diffuse phase boundaries.
Strong solutions in the dynamical theory of compressible fluid mixtures
2009, Kotschote, Matthias, Zacher, Rico
In this paper we investigate the compressible Navier-Stokes-Cahn-Hilliard equations (the so-called NSCH model) derived by Lowengrub and Truskinowsky. This model describes the flow of a binary compressible mixture; the fluids are supposed to be macroscopically immiscible, but partial mixing is permitted leading to narrow transition layers. The internal structure and macroscopic dynamics of these layers are induced by a Cahn-Hilliard law that the mixing ratio satisfies. The PDE constitute a strongly coupled hyperbolic-parabolic system. We establish a local existence and uniqueness result for strong solutions.