Existence and uniqueness of global weak solutions to a Cahn-Hilliard-Stokes-Darcy system for two phase incompressible flows in karstic geometry

TL;DR

This paper proves the existence and uniqueness of global weak solutions for a complex coupled system modeling two-phase incompressible flows in karstic geometries, advancing mathematical understanding of such fluid systems.

Contribution

It establishes the global existence and uniqueness of weak solutions for a coupled Cahn-Hilliard-Stokes-Darcy system in 2D and 3D, a novel result for this model.

Findings

Existence of global weak solutions in 2D and 3D

Weak-strong uniqueness property established

Mathematical well-posedness of the coupled system

Abstract

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.