The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations: An Introduction - Couverture souple

Bedrossian, Jacob; Vicol, Vlad

 
9781470471781: The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations: An Introduction
Couverture souple
ISBN 10 : 1470471787 ISBN 13 : 9781470471781
Editeur : American Mathematical Society, 2022

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Jacob Bedrossian, University of Maryland, College Park, MD.

Vlad Vicol, Courant Institute of Mathematical Sciences, New York University, NY.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2022
Langue
anglais
ISBN 10 
1470471787
ISBN 13 
9781470471781
Reliure
Broché
Nombre de pages
218
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9781470470494: The Mathematical Analysis of the Incompressible Euler and Navier-stokes Equations: An Introduction

Edition présentée

ISBN 10 :  1470470497 ISBN 13 :  9781470470494
Editeur : American Mathematical Society, 2022
Couverture rigide