Strong solutions in the dynamical theory of compressible fluid mixtures

2013/06/11 by Matthias Kotschote, Kotschote, Matthias, Rico Zacher +1 · 1 citation
Mathematics · Engineering · #Nonlinear Partial Differential Equations #Mathematical Dynamics and Fractals #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1306.2565

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.

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• Global weak solutions to a compressible Navier--Stokes/Cahn--Hilliard system with singular entropy of mixing

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