The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations write by Jacob Bedrossian. This book was released on 2022-09-21. The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations available in PDF, EPUB and Kindle. 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.
Recent Progress in the Theory of the Euler and Navier–Stokes Equations
Recent Progress in the Theory of the Euler and Navier–Stokes Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recent Progress in the Theory of the Euler and Navier–Stokes Equations write by James C. Robinson. This book was released on 2016-01-21. Recent Progress in the Theory of the Euler and Navier–Stokes Equations available in PDF, EPUB and Kindle. The rigorous mathematical theory of the Navier–Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier–Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive Burgers equations, and probabilistic aspects of the Navier–Stokes equation. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.
Vorticity and Incompressible Flow
Vorticity and Incompressible Flow - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Vorticity and Incompressible Flow write by Andrew J. Majda. This book was released on 2002. Vorticity and Incompressible Flow available in PDF, EPUB and Kindle. This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprise a modern applied mathematics graduate course on the weak solution theory for incompressible flow.
Handbook of Mathematical Fluid Dynamics
Handbook of Mathematical Fluid Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Handbook of Mathematical Fluid Dynamics write by S. Friedlander. This book was released on 2003-03-27. Handbook of Mathematical Fluid Dynamics available in PDF, EPUB and Kindle. The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
Introduction to the Numerical Analysis of Incompressible Viscous Flows
Introduction to the Numerical Analysis of Incompressible Viscous Flows - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to the Numerical Analysis of Incompressible Viscous Flows write by William Layton. This book was released on 2008-01-01. Introduction to the Numerical Analysis of Incompressible Viscous Flows available in PDF, EPUB and Kindle. Introduction to the Numerical Analysis of Incompressible Viscous Flows treats the numerical analysis of finite element computational fluid dynamics. Assuming minimal background, the text covers finite element methods; the derivation, behavior, analysis, and numerical analysis of Navier-Stokes equations; and turbulence and turbulence models used in simulations. Each chapter on theory is followed by a numerical analysis chapter that expands on the theory. This book provides the foundation for understanding the interconnection of the physics, mathematics, and numerics of the incompressible case, which is essential for progressing to the more complex flows not addressed in this book (e.g., viscoelasticity, plasmas, compressible flows, coating flows, flows of mixtures of fluids, and bubbly flows). With mathematical rigor and physical clarity, the book progresses from the mathematical preliminaries of energy and stress to finite element computational fluid dynamics in a format manageable in one semester. Audience: this unified treatment of fluid mechanics, analysis, and numerical analysis is intended for graduate students in mathematics, engineering, physics, and the sciences who are interested in understanding the foundations of methods commonly used for flow simulations.
