Global sharp interface limit of the Hele–Shaw–Cahn–Hilliard system

Abstract

In this paper, we focus on a diffuse interface model named by Hele–Shaw–Cahn–Hilliard system, which describes a two‐phase Hele–Shaw flow with matched densities and arbitrary viscosity contrast in a bounded domain. The diffuse interface thickness is measured by ϵ, and the mobility coefficient (the diffusional Peclet number) is ϵα. We will prove rigorously that the global weak solutions of the Hele–Shaw–Cahn–Hilliard system converge to a varifold solution of the sharp interface model as ϵ→0 in the case of 0≤α < 1. Copyright © 2016 John Wiley & Sons, Ltd.