Asymptotic Behavior of Weak Solutions of Non isothermal Flowofnon-Newtonian Fluid to Free Boundary / Maroua Lalmi

Public ISBD Titre : Asymptotic Behavior of Weak Solutions of Non isothermal Flowofnon-Newtonian Fluid to Free Boundary Type de document : texte imprimé Auteurs : Maroua Lalmi, Auteur ; Abdelkader Saadallah, Directeur de thèse Editeur : Sétif:UFA1 Année de publication : 2025 Importance : 1 vol (28 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Asymptotic approach Herschel-Bulkley fluid Temperature Reynolds equation Variational inequality Index. décimale : 510-Mathématique Résumé : The behavior of a Herschel-Bulkley fluid has been discussed in a thin layer in R3 associated with a nonlinear stationary, non-isothermal and incompressible model. Furthermore, the limit problem has been considered and the orig- inal problem in Ωε has been transformed into one posed over a fixed reference domain Ω independently of the parameter ε (ε being the parameter representing the thickness of the layer tending to zero). We also investigated the convergence of the unknowns which are the velocity, pressure and the temperature of the fluid. In addition, we established the limit problem and the specific Reynolds equation. Note de contenu : CONTENTS Introduction ii 1 Preliminairies and reminders 1 1.1 Tresca Type Friction Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Functional Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Some reminders of functional analysis. . . . . . . . . . . . . . . . . . . . . . 1 1.3.1 Lebesgue spaces: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3.2 Sobolev space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3.3 Vector-valued function spaces . . . . . . . . . . . . . . . . . . . . . 6 1.4 Lower semi-continuity properties. . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 Gronwall’s lemma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.6 Lemma minty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Asymptotic Behavior of Weak Solutions of Non isothermal Flow of non- Newtonian Fluid to Free Boundary 10 1.7 Statement of the problem and variational formulation . . . . . . . . . . . . 10 1.8 Change of the domain and study of convergence . . . . . . . . . . . . . . . . 13 1.8.1 A priori estimates on the velocity and the pressure . . . . . . . . . 15 1.8.2 A priori estimates on the temperature . . . . . . . . . . . . . . . . . 18 1.9 Study of the limit problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Bibliography 28 Côte titre : MAM/0775 Asymptotic Behavior of Weak Solutions of Non isothermal Flowofnon-Newtonian Fluid to Free Boundary [texte imprimé] / Maroua Lalmi, Auteur ; Abdelkader Saadallah, Directeur de thèse . - [S.l.] : Sétif:UFA1, 2025 . - 1 vol (28 f.) ; 29 cm. Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Asymptotic approach Herschel-Bulkley fluid Temperature Reynolds equation Variational inequality Index. décimale : 510-Mathématique Résumé : The behavior of a Herschel-Bulkley fluid has been discussed in a thin layer in R3 associated with a nonlinear stationary, non-isothermal and incompressible model. Furthermore, the limit problem has been considered and the orig- inal problem in Ωε has been transformed into one posed over a fixed reference domain Ω independently of the parameter ε (ε being the parameter representing the thickness of the layer tending to zero). We also investigated the convergence of the unknowns which are the velocity, pressure and the temperature of the fluid. In addition, we established the limit problem and the specific Reynolds equation. Note de contenu : CONTENTS Introduction ii 1 Preliminairies and reminders 1 1.1 Tresca Type Friction Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Functional Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.3 Some reminders of functional analysis. . . . . . . . . . . . . . . . . . . . . . 1 1.3.1 Lebesgue spaces: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3.2 Sobolev space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3.3 Vector-valued function spaces . . . . . . . . . . . . . . . . . . . . . 6 1.4 Lower semi-continuity properties. . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 Gronwall’s lemma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.6 Lemma minty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Asymptotic Behavior of Weak Solutions of Non isothermal Flow of non- Newtonian Fluid to Free Boundary 10 1.7 Statement of the problem and variational formulation . . . . . . . . . . . . 10 1.8 Change of the domain and study of convergence . . . . . . . . . . . . . . . . 13 1.8.1 A priori estimates on the velocity and the pressure . . . . . . . . . 15 1.8.2 A priori estimates on the temperature . . . . . . . . . . . . . . . . . 18 1.9 Study of the limit problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Bibliography 28 Côte titre : MAM/0775

Exemplaires (1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
MAM/0775	MAM/0775	Mémoire	Bibliothèque des sciences	Anglais	Disponible Disponible

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