The Mathematical Analysis of the Incompressible Euler and Navier-stokes Equations: An Introduction (Graduate Studies in Mathematics, 225)

<p>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.</p>

The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations (The Graduate Studies in Mathematics, 225)

Science & Math

Jacob Bedrossian

Vlad Vicol

Mathematics

American Mathematical Society

See the best price to sell, buy, or rent books by Vlad Vicol. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Vlad Vicol

See the best price to sell, buy, or rent books by Vlad Vicol. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations (The Graduate Studies in Mathematics, 225)