Handbook of Mathematical Analysis in Mechanics of Viscous Fluids PDF Download
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Author: Yoshikazu Giga
Publisher: Springer
ISBN: 9783319133430
Category : Mathematics
Languages : en
Pages : 2800
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Book Description
Mathematics has always played a key role for researches in fluid mechanics. The purpose of this handbook is to give an overview of items that are key to handling problems in fluid mechanics. Since the field of fluid mechanics is huge, it is almost impossible to cover many topics. In this handbook, we focus on mathematical analysis on viscous Newtonian fluid. The first part is devoted to mathematical analysis on incompressible fluids while part 2 is devoted to compressible fluids.
Author: Yoshikazu Giga
Publisher: Springer
ISBN: 9783319133430
Category : Mathematics
Languages : en
Pages : 2800
Get Book Here
Book Description
Mathematics has always played a key role for researches in fluid mechanics. The purpose of this handbook is to give an overview of items that are key to handling problems in fluid mechanics. Since the field of fluid mechanics is huge, it is almost impossible to cover many topics. In this handbook, we focus on mathematical analysis on viscous Newtonian fluid. The first part is devoted to mathematical analysis on incompressible fluids while part 2 is devoted to compressible fluids.
Author: Raphaël Danchin
Publisher: American Mathematical Soc.
ISBN: 1470436469
Category : Mathematics
Languages : en
Pages : 254
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Book Description
This volume contains the proceedings of the International Conference on Vorticity, Rotation and Symmetry (IV)—Complex Fluids and the Issue of Regularity, held from May 8–12, 2017, in Luminy, Marseille, France. The papers cover topics in mathematical fluid mechanics ranging from the classical regularity issue for solutions of the 3D Navier-Stokes system to compressible and non-Newtonian fluids, MHD flows and mixtures of fluids. Topics of different kinds of solutions, boundary conditions, and interfaces are also discussed.
Author: Roger Peyret
Publisher: Academic Press
ISBN: 0125530102
Category : Computers
Languages : en
Pages : 479
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Book Description
This handbook covers computational fluid dynamics from fundamentals to applications. This text provides a well documented critical survey of numerical methods for fluid mechanics, and gives a state-of-the-art description of computational fluid mechanics, considering numerical analysis, computer technology, and visualization tools. The chapters in this book are invaluable tools for reaching a deeper understanding of the problems associated with the calculation of fluid motion in various situations: inviscid and viscous, incompressible and compressible, steady and unsteady, laminar and turbulent flows, as well as simple and complex geometries. Each chapter includes a related bibliography Covers fundamentals and applications Provides a deeper understanding of the problems associated with the calculation of fluid motion
Author: Tohru Ozawa
Publisher: Springer Nature
ISBN: 3031192524
Category : Mathematics
Languages : en
Pages : 396
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Book Description
Yoshihiro Shibata has made many significant contributions to the area of mathematical fluid mechanics over the course of his illustrious career, including landmark work on the Navier-Stokes equations. The papers collected here — on the occasion of his 70th birthday — are written by world-renowned researchers and celebrate his decades of outstanding achievements.
Author: Matthias Hieber
Publisher: Springer Nature
ISBN: 3030362264
Category : Mathematics
Languages : en
Pages : 471
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Book Description
This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier–Stokes equations. As is well known, understanding the mathematical properties of these equations, along with their physical interpretation, constitutes one of the most challenging questions of applied mathematics. Indeed, the Navier-Stokes equations feature among the Clay Mathematics Institute's seven Millennium Prize Problems (existence of global in time, regular solutions corresponding to initial data of unrestricted magnitude). The text comprises three extensive contributions covering the following topics: (1) Operator-Valued H∞-calculus, R-boundedness, Fourier multipliers and maximal Lp-regularity theory for a large, abstract class of quasi-linear evolution problems with applications to Navier–Stokes equations and other fluid model equations; (2) Classical existence, uniqueness and regularity theorems of solutions to the Navier–Stokes initial-value problem, along with space-time partial regularity and investigation of the smoothness of the Lagrangean flow map; and (3) A complete mathematical theory of R-boundedness and maximal regularity with applications to free boundary problems for the Navier–Stokes equations with and without surface tension. Offering a general mathematical framework that could be used to study fluid problems and, more generally, a wide class of abstract evolution equations, this volume is aimed at graduate students and researchers who want to become acquainted with fundamental problems related to the Navier–Stokes equations.
Author: Jacob Bedrossian
Publisher: American Mathematical Society
ISBN: 1470470497
Category : Mathematics
Languages : en
Pages : 235
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Book 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.
Author: Tujin Kim
Publisher: Springer Nature
ISBN: 3030786595
Category : Mathematics
Languages : en
Pages : 374
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Book Description
This monograph explores the motion of incompressible fluids by presenting and incorporating various boundary conditions possible for real phenomena. The authors’ approach carefully walks readers through the development of fluid equations at the cutting edge of research, and the applications of a variety of boundary conditions to real-world problems. Special attention is paid to the equivalence between partial differential equations with a mixture of various boundary conditions and their corresponding variational problems, especially variational inequalities with one unknown. A self-contained approach is maintained throughout by first covering introductory topics, and then moving on to mixtures of boundary conditions, a thorough outline of the Navier-Stokes equations, an analysis of both the steady and non-steady Boussinesq system, and more. Equations of Motion for Incompressible Viscous Fluids is ideal for postgraduate students and researchers in the fields of fluid equations, numerical analysis, and mathematical modelling.
Author: Tomáš Bodnár
Publisher: Springer Nature
ISBN: 3031473558
Category :
Languages : en
Pages : 376
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Book Description
Author: Tomáš Bodnár
Publisher: Springer Nature
ISBN: 3030396398
Category : Mathematics
Languages : en
Pages : 647
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Book Description
This contributed volume is based on talks given at the August 2016 summer school “Fluids Under Pressure,” held in Prague as part of the “Prague-Sum” series. Written by experts in their respective fields, chapters explore the complex role that pressure plays in physics, mathematical modeling, and fluid flow analysis. Specific topics covered include: Oceanic and atmospheric dynamics Incompressible flows Viscous compressible flows Well-posedness of the Navier-Stokes equations Weak solutions to the Navier-Stokes equations Fluids Under Pressure will be a valuable resource for graduate students and researchers studying fluid flow dynamics.
Author: Tomáš Bodnár
Publisher: Springer Nature
ISBN: 3030681440
Category : Mathematics
Languages : en
Pages : 269
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Book Description
This volume explores a range of recent advances in mathematical fluid mechanics, covering theoretical topics and numerical methods. Chapters are based on the lectures given at a workshop in the summer school Waves in Flows, held in Prague from August 27-31, 2018. A broad overview of cutting edge research is presented, with a focus on mathematical modeling and numerical simulations. Readers will find a thorough analysis of numerous state-of-the-art developments presented by leading experts in their respective fields. Specific topics covered include: Chemorepulsion Compressible Navier-Stokes systems Newtonian fluids Fluid-structure interactions Waves in Flows: The 2018 Prague-Sum Workshop Lectures will appeal to post-doctoral students and scientists whose work involves fluid mechanics.
