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

2014/05/21 by Daozhi Han, Xiaoming Wang, Han, Daozhi +3 · 1 citation
Computer Science · Materials Science · Mathematics · #35K61 76T99 76S05 76D07 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1405.5415

openalex publication_date 2014/05/21 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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.

Citations

• Nonlinear Schrödinger evolution equations

Cited by

• Optimal L² error estimates of fully discrete finite element methods for the 2D/3D diffuse interface two-phase MHD flows

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