| Dewey Class |
532 |
| Title |
The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations ([Ebook]) : An Introduction / Jacon Bedrossian ; Vlad Vicol |
| Author |
Bedrossian, Jacob |
| Added Personal Name |
Vicol, Vlad |
| Publication |
Providence, Rhode Island : American Mathematical Society , 2022 |
| Physical Details |
1 online resource (xiii, 218 p., ill.) |
| Series |
Graduate studies in mathematics ; 225 |
| ISBN |
9781470471774 |
| Summary Note |
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. - provided by publisher: |
| Mode of acces to digital resource |
Digital reproduction.- Providence, Rhode Island : American Mathematical Society, 2022. - Mode of access : World Wide Web. - System requirements : Internet Explorer 6.0 (or higher) of Firefox 2.0 (or higher). Available as searchable text in PDF format |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address and through EbscoHost. Limited User Access (1 digital Copy Available ONLY for SISSA internal users) |
| Internet Site |
https://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=3374456&site=eds-live |
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