2013, Freistühler, Heinrich, Kotschote, Matthias

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.

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.