The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations: An Introduction (Graduate Studies in Mathematics) - Softcover

Jacob Bedrossian (author) & Vlad Vicol (author)

Softcover

ISBN 10: 1470471787 ISBN 13: 9781470471781

Publisher: 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.

About this title

About the Author

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

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

Edition details

• Publisher: American Mathematical Society
• Publication date: 2022
• Language: English
• ISBN 10: 1470471787
• ISBN 13: 9781470471781
• Binding: Paperback
• Number of pages: 218