Existence and Uniqueness of Global Weak Solutions to a Cahn-Hilliard-Stokes-Darcy System for Two Phase Incompressible Flows in Karstic Geometry
We study the well-posedness of a coupled Cahn-Hilliard-Stokes-Darcy system which is a diffuse-interface model for essentially immiscible two phase incompressible flows with matched density in a karstic geometry. Existence of finite energy weak solution that is global in time is established in both 2D and 3D. Weak-strong uniqueness property of the weak solutions is provided as well.
D. Han et al., "Existence and Uniqueness of Global Weak Solutions to a Cahn-Hilliard-Stokes-Darcy System for Two Phase Incompressible Flows in Karstic Geometry," Journal of Differential Equations, vol. 257, no. 10, pp. 3887-3933, Academic Press Inc., Nov 2014.
The definitive version is available at https://doi.org/10.1016/j.jde.2014.07.013
Mathematics and Statistics
Keywords and Phrases
Cahn-Hilliard-Stokes-Darcy system; Diffuse-interface model; Interface boundary conditions; Karstic geometry; Two phase flow; Well-posedness
International Standard Serial Number (ISSN)
Article - Journal
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