| Titre : |
The mathematical analysis of the incompressible Euler and Navier-Stokes equations : an introduction |
| Type de document : |
texte imprimé |
| Auteurs : |
Jacob Bedrossian, Auteur ; Vlad Vicol, Auteur |
| Editeur : |
Providence, R.I. [USA] : American Mathematical Society (AMS) |
| Année de publication : |
2022, cop. 2022 |
| Collection : |
Graduate studies in mathematics, ISSN 1065-7339 num. 225 |
| Importance : |
1 volume (xiii-218 p.) |
| Présentation : |
ill. en noir et en coul. |
| Format : |
27 cm |
| ISBN/ISSN/EAN : |
978-1-4704-7178-1 |
| Note générale : |
"for additional information and updates on this book, visit : www.ams.org/bookpages/gsm-225" -- PPN 271970715 |
| Langues : |
Anglais (eng) |
| Tags : |
Navier-Stokes, Équations de Euler, Équations d' Fluides incompressibles Fluides, Dynamique des Écoulement visqueux Navier-Stokes equation Fluid dynamics Viscous flow Incompressible fluids |
| Index. décimale : |
532.05 Dynamique des fluides |
| Résumé : |
The aim of this book is to provide beginning graduate students who completed the first two semesters of graduate-level analysis and PDE courses with a first exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces. Chapters 1 and 2 cover the fundamentals of the Euler theory: derivation, Eulerian and Lagrangian perspectives, vorticity, special solutions, existence theory for smooth solutions, and blowup criteria. Chapters 3, 4, and 5 cover the fundamentals of the Navier-Stokes theory: derivation, special solutions, existence theory for strong solutions, Leray theory of weak solutions, weak-strong uniqueness, existence theory of mild solutions, and Prodi-Serrin regularity criteria. Chapter 6 provides a short guide to the must-read topics, including active research directions, for an advanced graduate student working in incompressible fluids. It may be used as a roadmap for a topics course in a subsequent semester. The appendix recalls basic results from real, harmonic, and functional analysis. Each chapter concludes with exercises, making the text suitable for a one-semester graduate course. Prerequisites to this book are the first two semesters of graduate-level analysis and PDE courses. |
| Note de contenu : |
Bibliogr. p. 199-216. Index |
The mathematical analysis of the incompressible Euler and Navier-Stokes equations : an introduction [texte imprimé] / Jacob Bedrossian, Auteur ; Vlad Vicol, Auteur . - Providence, R.I. (USA) : American Mathematical Society (AMS), 2022, cop. 2022 . - 1 volume (xiii-218 p.) : ill. en noir et en coul. ; 27 cm. - ( Graduate studies in mathematics, ISSN 1065-7339; 225) . ISBN : 978-1-4704-7178-1 "for additional information and updates on this book, visit : www.ams.org/bookpages/gsm-225" -- PPN 271970715 Langues : Anglais ( eng)
| Tags : |
Navier-Stokes, Équations de Euler, Équations d' Fluides incompressibles Fluides, Dynamique des Écoulement visqueux Navier-Stokes equation Fluid dynamics Viscous flow Incompressible fluids |
| Index. décimale : |
532.05 Dynamique des fluides |
| Résumé : |
The aim of this book is to provide beginning graduate students who completed the first two semesters of graduate-level analysis and PDE courses with a first exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces. Chapters 1 and 2 cover the fundamentals of the Euler theory: derivation, Eulerian and Lagrangian perspectives, vorticity, special solutions, existence theory for smooth solutions, and blowup criteria. Chapters 3, 4, and 5 cover the fundamentals of the Navier-Stokes theory: derivation, special solutions, existence theory for strong solutions, Leray theory of weak solutions, weak-strong uniqueness, existence theory of mild solutions, and Prodi-Serrin regularity criteria. Chapter 6 provides a short guide to the must-read topics, including active research directions, for an advanced graduate student working in incompressible fluids. It may be used as a roadmap for a topics course in a subsequent semester. The appendix recalls basic results from real, harmonic, and functional analysis. Each chapter concludes with exercises, making the text suitable for a one-semester graduate course. Prerequisites to this book are the first two semesters of graduate-level analysis and PDE courses. |
| Note de contenu : |
Bibliogr. p. 199-216. Index |
|
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