On the Doubly Non-local Hele-Shaw-Cahn-Hilliard System: Derivation and 2D Well-Posedness

被引：0

作者：

Peter, Malte A. ^{[1
,2
]}

Woukeng, Jean Louis ^{[1
,3
]}

机构：

[1] Univ Augsburg, Inst Math, Univ Str 12a, D-86159 Augsburg, Germany

[2] Univ Augsburg, Ctr Adv Analyt & Predict Sci, Univ Str 12a, D-86159 Augsburg, Germany

[3] Univ Dschang, Dept Math & Comp Sci, POB 67, Dschang, Cameroon

来源：

JOURNAL OF NONLINEAR SCIENCE | 2024年 / 34卷 / 03期

关键词：

Non-local Cahn-Hilliard-Stokes system; Sigma-convergence; Thin domains; Doubly non-local Hele-Shaw-Cahn-Hilliard system; Homogenization; EFFECTIVE TRANSMISSION CONDITIONS; DIFFUSE INTERFACE MODEL; NAVIER-STOKES SYSTEMS; LONG-TIME BEHAVIOR; POROUS-MEDIA; HOMOGENIZATION; EQUATIONS; DOMAINS; CONVERGENCE; SIMULATION;

D O I：

10.1007/s00332-024-10018-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Starting from a classic non-local (in space) Cahn-Hilliard-Stokes model for two-phase flow in a thin heterogeneous fluid domain, we rigorously derive by mathematical homogenization a new effective mixture model consisting of a coupling of a non-local (in time) Hele-Shaw equation with a non-local (in space) Cahn-Hilliard equation. We then analyse the resulting model and prove its well-posedness. A key to the analysis is the new concept of sigma-convergence in thin heterogeneous domains allowing to pass to the homogenization limit with respect to the heterogeneities and the domain thickness simultaneously.

引用

页数：56

共 56 条

[1] Diffuse interface models of locally inextensible vesicles in a viscous fluid [J].