MATHEMATICAL PROPERTIES OF FLOWS OF INCOMPRESSIBLE POWER-LAW-LIKE FLUIDS THAT ARE DESCRIBED BY IMPLICIT CONSTITUTIVE RELATIONS

被引：0

作者：

Malek, Josef ^{[1
,2
]}

机构：

[1] Charles Univ Prague, Math Inst, Prague 18675 8, Czech Republic

[2] Acad Sci Czech Republic, Inst Thermomech, Prague 18200 8, Czech Republic

来源：

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2008年 / 31卷

关键词：

Power-law fluid; incompressible fluid; implicit constitutive theory; Rothe approximation; time discretization; weak solution; existence; regularity;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We report on very recent developments concerning the modelling of the complex behaviour of materials within the framework of implicit constitutive theory due to K. R. Rajagopal. In this paper, we restrict ourselves to a hierarchy of power-law-like fluids. For such a class of fluids, we provide an overview of recent results concerning the mathematical analysis of the relevant boundary value problems. Mathematical results are presented for the (Rothe) time discretizations of evolutionary problems. The main purpose of this paper is to emphasize the mathematical tools involved in the theoretical analysis and to initiate the development of numerical methods for the problems presented here.

引用

页码：110 / 125

页数：16

共 18 条

[1] On steady flows of incompressible fluids with implicit power-law-like rheology
Bulicek, Miroslav
Gwiazda, Piotr
Malek, Josef
Swierczewska-Gwiazda, Agnieszka
[J]. ADVANCES IN CALCULUS OF VARIATIONS, 2009, 2 (02) : 109 - 136
[2] FINITE ELEMENT APPROXIMATION OF STEADY FLOWS OF INCOMPRESSIBLE FLUIDS WITH IMPLICIT POWER-LAW-LIKE RHEOLOGY
Diening, Lars
Kreuzer, Christian
Sueli, Endre
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2013, 51 (02) : 984 - 1015
[3] ADAPTIVE FINITE ELEMENT APPROXIMATION OF STEADY FLOWS OF INCOMPRESSIBLE FLUIDS WITH IMPLICIT POWER-LAW-LIKE RHEOLOGY
Kreuzer, Christian
Suli, Endre
[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2016, 50 (05): : 1333 - 1369
[4] On flows of an incompressible fluid with a discontinuous power-law-like rheology
Gwiazda, Piotr
Malek, Josef
Swierczewska, Agnieszka
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 53 (3-4) : 531 - 546
[5] Tensorial implicit constitutive relations in mechanics of incompressible non-Newtonian fluids
Perlacova, Tereza
Pruga, Vit
[J]. JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 2015, 216 : 13 - 21
[6] On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary
Bulicek, Miroslav
Malek, Josef
Maringova, Erika
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2023, 25 (03)
[7] On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary
Miroslav Bulíček
Josef Málek
Erika Maringová
[J]. Journal of Mathematical Fluid Mechanics, 2023, 25
[8] Implicit Type Constitutive Relations for Elastic Solids and Their Use in the Development of Mathematical Models for Viscoelastic Fluids
Prusa, Vit
Rajagopal, K. R.
[J]. FLUIDS, 2021, 6 (03)
[9] On the Flows of Fluids Defined through Implicit Constitutive Relations between the Stress and the Symmetric Part of the Velocity Gradient
Rajagopal, Kumbakonam R.
[J]. FLUIDS, 2016, 1 (02):
[10] Improved Implicit SPH Method for simulating free surface flows of power law fluids
Han YaWei
Qiang HongFu
Huang QuanZhang
Zhao JiuLing
[J]. SCIENCE CHINA-TECHNOLOGICAL SCIENCES, 2013, 56 (10) : 2480 - 2490

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