The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations: An Introduction - Brossura
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In a textbook for beginning graduate students, Bedrossian and Vicol briefly introduce the mathematical analysis of the incompressible Euler and incompressible Navier-Stokes equations. They assume students have completed their first one or two semesters of graduate-level analysis and partial differential equations, but not necessarily any further partial differential equation courses. The material can be used in a semester graduate course or for individual study, they say. They cover 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, and a survey of some advanced topics. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)
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The Mathematical Analysis of the Incompressible - An Introduction (eng)
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The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations
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ISBN 13: 9781470471781
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Paperback. Condizione: New. 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. Codice articolo LU-9781470471781
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Paperback. Condizione: new. Paperback. 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. Provides graduate students with 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9781470471781
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The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations: An Introduction
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The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations: An Introduction
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