Titre :	A Study of Various Free Boundary Value Problems in Fluid Mechanics : The Asymptotic Behavior of Weak Solution
Type de document :	document électronique
Auteurs :	Malek Abdelali, Auteur ; Saadallah ,Abdelkader, Directeur de thèse
Editeur :	Setif:UFA
Année de publication :	2025
Importance :	1 vol (93 f.)
Format :	29 cm
Langues :	Anglais (eng)
Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Asymptotic approach Bingham fluid Herschel-Bulkley fluid Temperature Reynolds equation
Index. décimale :	510 - Mathématique
Résumé :	This thesis investigates the asymptotic behavior of non-isothermal flows of viscoplastic fluids (Bingham and Herschel-Bulkley) in thin domains with Tresca-type friction conditions. An effective limit model is derived, combining a Reynolds-type variational inequality with a simplified heat equation. The analysis rigorously proves the existence, uniqueness, and convergence of solutions. These results establish a robust mathematical framework for simulating confined flows, with significant applications in lubrication engineering and process design.
Note de contenu :	Sommaire 0.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 Formulation of Boundary Problems and Preliminaries 8 1.1 Mathematical formulation of boundary value problems . . . . . . . . . . . 9 1.1.1 Constitutive Law of the Bingham Fluid . . . . . . . . . . . . . . . . 9 1.1.2 Constitutive Law of the Herschel–Bulkley Fluid . . . . . . . . . . . 13 1.1.3 Sliding with Tresca Friction Law . . . . . . . . . . . . . . . . . . . 15 1.1.4 Energy Conservation Equation and Fourier Boundary Conditions . 16 1.1.5 Steady-State Thermal Flow of a Bingham Fluid under Tresca-Type Frictional Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.1.6 Steady-State Thermal Flow of a Herschel–Bulkley Fluid under Tresca- Type Frictional Contact . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2 Review of Mathematical Analysis . . . . . . . . . . . . . . . . . . . . . . . 21 1.2.1 Sobolev Spaces and Lp Spaces . . . . . . . . . . . . . . . . . . . . . 21 1.2.2 Minty’s Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.2.3 Fundamental Inequalities . . . . . . . . . . . . . . . . . . . . . . . 23 2 Stationary Solutions of Non-Isothermal Bingham Flow with Nonlinear Boundary Conditions in a Thin Domain 25 2.1 Introduction and Problem Statement . . . . . . . . . . . . . . . . . . . . . 25 2.2 Variational Problem and Existence Results . . . . . . . . . . . . . . . . . . 29 2.2.1 Functional Framework and Variational Formulation . . . . . . . . . 31 2.3 Domain Transformation and A Priori Estimates . . . . . . . . . . . . . . . 35 2.3.1 Change of Reference Domain . . . . . . . . . . . . . . . . . . . . . 35 2.3.2 Variational Formulation on Ω . . . . . . . . . . . . . . . . . . . . . 36 2.3.3 A Priori Estimates for Velocity and Pressure . . . . . . . . . . . . . 38 2.3.4 A Priori Estimates for Temperature . . . . . . . . . . . . . . . . . . 42 2.4 Study of the Limit Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3 Asymptotic Behavior of Solutions for a Non-Isothermal Coupled Problem With Nonlinear Boundary Conditions in a Thin Domain 58 3.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2 Weak formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.3 Change of the domain and study of convergence . . . . . . . . . . . . . . . 64 3.3.1 A priori estimates on the velocity and the pressure . . . . . . . . . 68 3.3.2 A priori estimates on the temperature . . . . . . . . . . . . . . . . 69 3.3.3 Theorem of Convergence . . . . . . . . . . . . . . . . . . . . . . . 74 3.4 Study of the Limit Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.4.1 Limit Problem and the Generalized Reynolds Equation . . . . . . . 77 3.4.2 Uniqueness of Solutions to the Limit Problem . . . . . . . . . . . . 85 Bibliographie 88
Côte titre :	DM/0219

A Study of Various Free Boundary Value Problems in Fluid Mechanics : The Asymptotic Behavior of Weak Solution [document électronique] / Malek Abdelali, Auteur ; Saadallah ,Abdelkader, Directeur de thèse . - [S.l.] : Setif:UFA, 2025 . - 1 vol (93 f.) ; 29 cm.
Langues : Anglais (eng)

Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Asymptotic approach Bingham fluid Herschel-Bulkley fluid Temperature Reynolds equation
Index. décimale :	510 - Mathématique
Résumé :	This thesis investigates the asymptotic behavior of non-isothermal flows of viscoplastic fluids (Bingham and Herschel-Bulkley) in thin domains with Tresca-type friction conditions. An effective limit model is derived, combining a Reynolds-type variational inequality with a simplified heat equation. The analysis rigorously proves the existence, uniqueness, and convergence of solutions. These results establish a robust mathematical framework for simulating confined flows, with significant applications in lubrication engineering and process design.
Note de contenu :	Sommaire 0.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 Formulation of Boundary Problems and Preliminaries 8 1.1 Mathematical formulation of boundary value problems . . . . . . . . . . . 9 1.1.1 Constitutive Law of the Bingham Fluid . . . . . . . . . . . . . . . . 9 1.1.2 Constitutive Law of the Herschel–Bulkley Fluid . . . . . . . . . . . 13 1.1.3 Sliding with Tresca Friction Law . . . . . . . . . . . . . . . . . . . 15 1.1.4 Energy Conservation Equation and Fourier Boundary Conditions . 16 1.1.5 Steady-State Thermal Flow of a Bingham Fluid under Tresca-Type Frictional Contact . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.1.6 Steady-State Thermal Flow of a Herschel–Bulkley Fluid under Tresca- Type Frictional Contact . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2 Review of Mathematical Analysis . . . . . . . . . . . . . . . . . . . . . . . 21 1.2.1 Sobolev Spaces and Lp Spaces . . . . . . . . . . . . . . . . . . . . . 21 1.2.2 Minty’s Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.2.3 Fundamental Inequalities . . . . . . . . . . . . . . . . . . . . . . . 23 2 Stationary Solutions of Non-Isothermal Bingham Flow with Nonlinear Boundary Conditions in a Thin Domain 25 2.1 Introduction and Problem Statement . . . . . . . . . . . . . . . . . . . . . 25 2.2 Variational Problem and Existence Results . . . . . . . . . . . . . . . . . . 29 2.2.1 Functional Framework and Variational Formulation . . . . . . . . . 31 2.3 Domain Transformation and A Priori Estimates . . . . . . . . . . . . . . . 35 2.3.1 Change of Reference Domain . . . . . . . . . . . . . . . . . . . . . 35 2.3.2 Variational Formulation on Ω . . . . . . . . . . . . . . . . . . . . . 36 2.3.3 A Priori Estimates for Velocity and Pressure . . . . . . . . . . . . . 38 2.3.4 A Priori Estimates for Temperature . . . . . . . . . . . . . . . . . . 42 2.4 Study of the Limit Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3 Asymptotic Behavior of Solutions for a Non-Isothermal Coupled Problem With Nonlinear Boundary Conditions in a Thin Domain 58 3.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2 Weak formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.3 Change of the domain and study of convergence . . . . . . . . . . . . . . . 64 3.3.1 A priori estimates on the velocity and the pressure . . . . . . . . . 68 3.3.2 A priori estimates on the temperature . . . . . . . . . . . . . . . . 69 3.3.3 Theorem of Convergence . . . . . . . . . . . . . . . . . . . . . . . 74 3.4 Study of the Limit Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.4.1 Limit Problem and the Generalized Reynolds Equation . . . . . . . 77 3.4.2 Uniqueness of Solutions to the Limit Problem . . . . . . . . . . . . 85 Bibliographie 88
Côte titre :	DM/0219