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Author : Yoshikazu Giga,Antonín Novotný
Publisher : Unknown
Page : 128 pages
File Size : 43,9 Mb
Release : 2018
Category : Electronic
ISBN : OCLC:1040276601
Author : Eduard Feireisl,Trygve G. Karper,Milan Pokorný
Publisher : Birkhäuser
Page : 186 pages
File Size : 53,5 Mb
Release : 2016-11-25
Category : Mathematics
ISBN : 9783319448350
This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematics. It will help graduate students and researchers to not only better understand problems in mathematical compressible fluid mechanics but also to learn something from the field of mathematical and numerical analysis and to see the connections between the two worlds. Potential readers should possess a good command of the basic tools of functional analysis and partial differential equations including the function spaces of Sobolev type.
Author : S. Friedlander,D. Serre
Publisher : Gulf Professional Publishing
Page : 627 pages
File Size : 55,5 Mb
Release : 2003-03-27
Category : Science
ISBN : 9780080533544
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.
Author : Raphaël Danchin,Reinhard Farwig,Jiří Neustupa,Patrick Penel
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 42,6 Mb
Release : 2018-06-26
Category : Fluid mechanics
ISBN : 9781470436469
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 : D. Cioranescu,V. Girault,K.R. Rajagopal
Publisher : Springer
Page : 394 pages
File Size : 49,8 Mb
Release : 2016-07-29
Category : Science
ISBN : 9783319393308
This text is the first of its kind to bring together both the thermomechanics and mathematical analysis of Reiner-Rivlin fluids and fluids of grades 2 and 3 in a single book. Each part of the book can be considered as being self-contained. The first part of the book is devoted to a description of the mechanics, thermodynamics, and stability of flows of fluids of grade 2 and grade 3. The second part of the book is dedicated to the development of rigorous mathematical results concerning the equations governing the motion of a family of fluids of the differential type. Finally, the proofs of a number of useful results are collected in an appendix.
Author : Yoshikazu Giga,Antonin Novotny
Publisher : Springer
Page : 2800 pages
File Size : 50,5 Mb
Release : 2018-01-26
Category : Mathematics
ISBN : 3319133438
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 : Tohru Ozawa
Publisher : Springer Nature
Page : 396 pages
File Size : 51,8 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 9783031192524
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,James C. Robinson,Yoshihiro Shibata
Publisher : Springer Nature
Page : 471 pages
File Size : 55,7 Mb
Release : 2020-04-28
Category : Mathematics
ISBN : 9783030362263
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,Vlad Vicol
Publisher : American Mathematical Society
Page : 235 pages
File Size : 45,6 Mb
Release : 2022-09-21
Category : Mathematics
ISBN : 9781470470494
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,Daomin Cao
Publisher : Springer Nature
Page : 374 pages
File Size : 45,6 Mb
Release : 2021-09-09
Category : Mathematics
ISBN : 9783030786595
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 : Denise Campos (Editor)
Publisher : Unknown
Page : 508 pages
File Size : 53,5 Mb
Release : 2016
Category : MATHEMATICS
ISBN : 153610308X
Author : William Layton
Publisher : SIAM
Page : 220 pages
File Size : 40,5 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780898718904
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.
Author : Tomáš Bodnár,Giovanni P. Galdi,Šárka Nečasová
Publisher : Springer Nature
Page : 647 pages
File Size : 43,9 Mb
Release : 2020-04-30
Category : Mathematics
ISBN : 9783030396398
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 : Hilary Ockendon,J. R. Ockendon
Publisher : Cambridge University Press
Page : 130 pages
File Size : 54,8 Mb
Release : 1995-01-27
Category : Mathematics
ISBN : 0521458811
Many of the topics in inviscid fluid dynamics are not only vitally important mechanisms in everyday life but they are also readily observable without any need for instrumentation. It is therefore stimulating when the mathematics that emerges when these phenomena are modelled is novel and suggestive of alternative methodologies. This book provides senior undergraduates who are already familiar with inviscid fluid dynamics with some of the basic facts about the modelling and analysis of viscous flows. It clearly presents the salient physical ideas and the mathematical ramifications with exercises designed to be an integral part of the text. By showing the basic theoretical framework which has developed as a result of the study of viscous flows, the book should be ideal reading for students of applied mathematics who should then be able to delve further into the subject and be well placed to exploit mathematical ideas throughout the whole of applied science.
Author : Frank H. Berkshire,Simon J. A. Malham,J. Trevor Stuart
Publisher : Cambridge University Press
Page : 335 pages
File Size : 53,5 Mb
Release : 2021-12-02
Category : Science
ISBN : 9781316513736
This textbook gives a comprehensive, accessible introduction to the mathematics of incompressible fluid mechanics and its many applications.
