Weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities and nonlocal free energies

被引：6

作者：

Abels, Helmut ^{[1
]}

Terasawa, Yutaka ^{[2
]}

机构：

[1] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

[2] Nagoya Univ, Grad Sch Math, Nagoya, Aichi, Japan

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2020年 / 43卷 / 06期

基金：

日本学术振兴会;

关键词：

Cahn-Hilliard equation; diffuse interface model; mixtures of viscous fluids; Navier-Stokes equation; nonlocal operators; two-phase flow; PHASE SEGREGATION DYNAMICS; LONG-RANGE INTERACTIONS; CAHN-HILLIARD EQUATION; PARTICLE-SYSTEMS; CONVERGENCE; EXISTENCE;

D O I：

10.1002/mma.6111

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a diffuse interface model for the flow of two viscous incompressible Newtonian fluids with different densities in a bounded domain in two and three space dimensions and prove existence of weak solutions for it. In contrast to earlier contributions, we study a model with a singular nonlocal free energy, which controls the H-alpha/2-norm of the volume fraction. We show existence of weak solutions for large times with the aid of an implicit time discretization.

引用

页码：3200 / 3219

页数：20

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