Existence and Weak-Strong Uniqueness of Solutions to the Cahn-Hilliard-Navier-Stokes-Darcy System in Superposed Free Flow and Porous Media
We study a diffuse interface model for two-phase flows of similar densities in superposed free flow and porous media. The model consists of the Navier-Stokes-Cahn-Hilliard system in free flow and the Darcy-Cahn-Hilliard system in porous media coupled through a set of domain interface boundary conditions. These domain interface boundary conditions include the nonlinear Lions interface condition and the linear Beavers-Joseph-Saffman-Jones interface condition. We establish global existence of weak solutions in three dimension. We also show that the strong solution if exists agrees with the weak solutions.
D. Han et al., "Existence and Weak-Strong Uniqueness of Solutions to the Cahn-Hilliard-Navier-Stokes-Darcy System in Superposed Free Flow and Porous Media," Nonlinear Analysis, Theory, Methods and Applications, vol. 211, article no. 112411, Elsevier, Oct 2021.
The definitive version is available at https://doi.org/10.1016/j.na.2021.112411
Mathematics and Statistics
Keywords and Phrases
Cahn-Hilliard; Darcy; Diffuse interface model; Navier-Stokes; Superposed free flow and porous media; Well-posedness
International Standard Serial Number (ISSN)
Article - Journal
© 2021 Elsevier, All rights reserved.
01 Oct 2021