GLOBAL SOLUTIONS OF A DIFFUSE INTERFACE MODEL FOR THE TWO-PHASE FLOW OF COMPRESSIBLE VISCOUS FLUIDS IN 1D

被引：0

作者：

Ding, Shijin ^{[1
]}

Li, Yinghua ^{[1
]}

机构：

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2020年 / 18卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Compressible; Navier-Stokes; Cahn-Hilliard; Global solutions; NAVIER-STOKES EQUATIONS; PHASE-FIELD MODEL; INCOMPRESSIBLE FLUIDS; CLASSICAL-SOLUTIONS; EXISTENCE; DENSITY; ENERGY; SYSTEM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with a coupled Navier-Stokes/Cahn-Hilliard system describing a diffuse interface model for the two-phase flow of compressible viscous fluids in a bounded domain in one dimension. We prove the existence and uniqueness of global classical solutions for rho(0) is an element of C-3,C-alpha(I). Moreover, we also obtain the global existence of weak solutions and unique strong solutions for rho(0) is an element of H-1(I) and rho(0) is an element of H-2(I), respectively. In these cases, the initial density function rho(0) has a positive lower bound.

引用

页码：1055 / 1086

页数：32

共 36 条

[1] On a diffuse interface model for a two-phase flow of compressible viscous fluids [J].

Abels, Helmut ;

Feireisl, Eduard .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (02) :659-698

[2] Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities [J].

Abels, Helmut ;

Depner, Daniel ;

Garcke, Harald .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2013, 15 (03) :453-480

[3] THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES [J].

Abels, Helmut ;

Garcke, Harald ;

Gruen, Guenther .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2012, 22 (03)

[4] Existence of Weak Solutions for a Diffuse Interface Model for Viscous, Incompressible Fluids with General Densities [J].

Abels, Helmut .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2009, 289 (01) :45-73

[5] On a Diffuse Interface Model for Two-Phase Flows of Viscous, Incompressible Fluids with Matched Densities [J].

Abels, Helmut .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2009, 194 (02) :463-506

[6] Diffuse-interface methods in fluid mechanics [J].

Anderson, DM ;

McFadden, GB ;

Wheeler, AA .

ANNUAL REVIEW OF FLUID MECHANICS, 1998, 30 :139-165

[7] A generalization of the Navier-Stokes equations to two-phase flows [J].

Blesgen, T .

JOURNAL OF PHYSICS D-APPLIED PHYSICS, 1999, 32 (10) :1119-1123

[8] A theoretical and numerical model for the study of incompressible mixture flows [J].

Boyer, F .

COMPUTERS & FLUIDS, 2002, 31 (01) :41-68

[9] Nonhomogeneous Cahn-Hilliard fluids [J].

Boyer, F .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2001, 18 (02) :225-259

[10]

Boyer F, 1999, ASYMPTOTIC ANAL, V20, P175

← 1 2 3 4 →