The mathematical analysis of the incompressible Euler and Navier-Stokes equations : an introduction

Author(s)

• Bedrossian, Jacob
• Vicol, Vlad

Bibliographic Information

The mathematical analysis of the incompressible Euler and Navier-Stokes equations : an introduction

Jacob Bedrossian, Vlad Vicol

（Graduate studies in mathematics, 225）

American Mathematical Society, c2022

Note

"Applied mathematics"--On cover

Includes bibliographical references (p. 199-216) and index

Description and Table of Contents

Description

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.

Table of Contents

Ideal incompressible fluids: The Euler equations Existence of solutions and continuation criteria for Euler Incompressible viscous fluids: The Navier-Stokes equations Leray-Hopf weak solutions of Navier-Stokes Mild solutions of Navier-Stokes A survey of some advanced topics Appendix Bibliography Index

by "Nielsen BookData"

• NCID: BC17008424
• ISBN:
  • 9781470470494
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: xiii, 218 p.
• Size: 27 cm
• Classification:
  • LCC : QA911
  • DC23 : 532/.050151864
  • DC23 : 532.050151864
• Subject Headings:
  • LCSH : Fluid dynamics
  • LCSH : Navier-Stokes equations
• Parent Bibliography ID:
  • BA20542214