Strong solutions in the dynamical theory of compressible fluid mixtures

TL;DR

This paper establishes local existence and uniqueness of strong solutions for the coupled hyperbolic-parabolic PDE system modeling compressible fluid mixtures via the Navier-Stokes-Cahn-Hilliard equations.

Contribution

It provides the first rigorous proof of strong solutions' existence and uniqueness for the NSCH model describing compressible binary fluid mixtures.

Findings

Proved local existence of strong solutions.

Established uniqueness of solutions.

Analyzed the coupled hyperbolic-parabolic system.

Abstract

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.