Mixing rules and the Navier-Stokes-Cahn-Hilliard equations for compressible heat-conductive fluids. (English) Zbl 1354.76039
Summary: The framework of this article is the compressible Navier-Stokes-Cahn-Hilliard system for the dynamics of a fluid whose two phases are macroscopically immiscible; partial mixing is permitted leading to narrow transition layers. This so-called NSCH model was originally derived by J. Lowengrub and L. Truskinovsky [Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 454, No. 1978, 2617–2654 (1998; Zbl 0927.76007)], but only for the isothermal case. The purpose of this work is to present the non-isothermal version as well as a well-posedness result. The PDEs constitute a strongly coupled hyperbolicparabolic system.
MSC:
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35D35 | Strong solutions to PDEs |
| 35K30 | Initial value problems for higher-order parabolic equations |
Keywords:
Navier-Stokes-Cahn-Hilliard equations; compressible fluids; immiscible binary fluids; diffuse interfaces; hyperbolic-parabolic systemsCitations:
Zbl 0927.76007References:
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