Mathematical Analysis Of The Navier Stokes Equations

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Mathematical Analysis of the Navier-Stokes Equations

Matthias Hieber,James C. Robinson,Yoshihiro Shibata
Mathematical Analysis of the Navier Stokes Equations Book PDF

Author : Matthias Hieber,James C. Robinson,Yoshihiro Shibata
Publisher : Springer Nature
Page : 471 pages
File Size : 41,7 Mb
Release : 2020-04-28
Category : Mathematics
ISBN : 9783030362263

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Mathematical Analysis of the Navier-Stokes Equations by Matthias Hieber,James C. Robinson,Yoshihiro Shibata Pdf

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.

Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models

Franck Boyer,Pierre Fabrie
Mathematical Tools for the Study of the Incompressible Navier Stokes Equations andRelated Models Book PDF

Author : Franck Boyer,Pierre Fabrie
Publisher : Springer Science & Business Media
Page : 538 pages
File Size : 48,9 Mb
Release : 2012-11-06
Category : Mathematics
ISBN : 9781461459750

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Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models by Franck Boyer,Pierre Fabrie Pdf

The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .

Navier-Stokes Flow Around a Rotating Obstacle

Sarka Necasova,Stanislav Kracmar
Navier Stokes Flow Around a Rotating Obstacle Book PDF

Author : Sarka Necasova,Stanislav Kracmar
Publisher : Springer
Page : 96 pages
File Size : 55,5 Mb
Release : 2016-10-06
Category : Mathematics
ISBN : 9789462392311

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Navier-Stokes Flow Around a Rotating Obstacle by Sarka Necasova,Stanislav Kracmar Pdf

The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of problems arising from the motion of viscous incompressible fluids around rotating obstacles. It offers a new approach to this type of problems. We derive the fundamental solution of the steady case and we give pointwise estimates of velocity and its gradient (first and second one). Each chapter is preceded by a thorough discussion of the investigated problems, along with their motivation and the strategy used to solve them.The book will be useful to researchers and graduate students in mathematics, in particular mathematical fluid mechanics and differential equations.

Applied Analysis of the Navier-Stokes Equations

Charles R. Doering,J. D. Gibbon
Applied Analysis of the Navier Stokes Equations Book PDF

Author : Charles R. Doering,J. D. Gibbon
Publisher : Cambridge University Press
Page : 236 pages
File Size : 41,9 Mb
Release : 1995
Category : Mathematics
ISBN : 052144568X

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Applied Analysis of the Navier-Stokes Equations by Charles R. Doering,J. D. Gibbon Pdf

This introductory physical and mathematical presentation of the Navier-Stokes equations focuses on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion.

Navier—Stokes Equations

Roger Temam
Navier Stokes Equations Book PDF

Author : Roger Temam
Publisher : Elsevier
Page : 530 pages
File Size : 45,9 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483256856

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Navier—Stokes Equations by Roger Temam Pdf

Navier-Stokes Equations: Theory and Numerical Analysis focuses on the processes, methodologies, principles, and approaches involved in Navier-Stokes equations, computational fluid dynamics (CFD), and mathematical analysis to which CFD is grounded. The publication first takes a look at steady-state Stokes equations and steady-state Navier-Stokes equations. Topics include bifurcation theory and non-uniqueness results, discrete inequalities and compactness theorems, existence and uniqueness theorems, discretization of Stokes equations, existence and uniqueness for the Stokes equations, and function spaces. The text then examines the evolution of Navier-Stokes equations, including linear case, compactness theorems, alternate proof of existence by semi-discretization, and discretization of the Navier-Stokes equations. The book ponders on the approximation of the Navier-Stokes equations by the projection and compressibility methods; properties of the curl operator and application to the steady-state Navier-Stokes equations; and implementation of non-conforming linear finite elements. The publication is a valuable reference for researchers interested in the theory and numerical analysis of Navier-Stokes equations.

An Introduction to the Mathematical Theory of the Navier-Stokes Equations

Giovanni Galdi
An Introduction to the Mathematical Theory of the Navier Stokes Equations Book PDF

Author : Giovanni Galdi
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 47,9 Mb
Release : 2013-03-14
Category : Science
ISBN : 9781475738667

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An Introduction to the Mathematical Theory of the Navier-Stokes Equations by Giovanni Galdi Pdf

Undoubtedly, the Navier-Stokes equations are of basic importance within the context of modern theory of partial differential equations. Although the range of their applicability to concrete problems has now been clearly recognised to be limited, as my dear friend and bright colleague K.R. Ra jagopal has showed me by several examples during the past six years, the mathematical questions that remain open are of such a fascinating and challenging nature that analysts and applied mathematicians cannot help being attracted by them and trying to contribute to their resolution. Thus, it is not a coincidence that over the past ten years more than seventy sig nificant research papers have appeared concerning the well-posedness of boundary and initial-boundary value problems. In this monograph I shall perform a systematic and up-to-date investiga tion of the fundamental properties of the Navier-Stokes equations, including existence, uniqueness, and regularity of solutions and, whenever the region of flow is unbounded, of their spatial asymptotic behavior. I shall omit other relevant topics like boundary layer theory, stability, bifurcation, de tailed analysis of the behavior for large times, and free-boundary problems, which are to be considered "advanced" ones. In this sense the present work should be regarded as "introductory" to the matter.

Navier-Stokes Equations: A Mathematical Analysis

Giovanni P. Galdi
Navier Stokes Equations A Mathematical Analysis Book PDF

Author : Giovanni P. Galdi
Publisher : Birkhäuser
Page : 495 pages
File Size : 40,6 Mb
Release : 2017
Category : Mathematics
ISBN : 3034804830

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Navier-Stokes Equations: A Mathematical Analysis by Giovanni P. Galdi Pdf

The Navier-Stokes equations - modeling the motion of viscous, incompressible Newtonian fluids - have been capturing the attention of an increasing number of mathematicians over the years and has now become one of the most intensely studied subjects in applied analysis. This project is dedicated to a complete and updated mathematical analysis of fundamental topics related to these equations. Every subject will be analyzed using different approaches. The main ideas behind them as well as their differences will also be emphasized and discussed. The book aims at being self-contained, however, it will also be supported by a vast bibliography for further reading.

The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations

Jacob Bedrossian,Vlad Vicol
The Mathematical Analysis of the Incompressible Euler and Navier Stokes Equations Book PDF

Author : Jacob Bedrossian,Vlad Vicol
Publisher : American Mathematical Society
Page : 235 pages
File Size : 48,8 Mb
Release : 2022-09-22
Category : Mathematics
ISBN : 9781470471781

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The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations by Jacob Bedrossian,Vlad Vicol Pdf

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.

Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models

Franck Boyer,Pierre Fabrie
Mathematical Tools for the Study of the Incompressible Navier Stokes Equations and Related Models Book PDF

Author : Franck Boyer,Pierre Fabrie
Publisher : Springer
Page : 526 pages
File Size : 50,7 Mb
Release : 2012-11-06
Category : Mathematics
ISBN : 1461459761

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Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models by Franck Boyer,Pierre Fabrie Pdf

The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .

Observability and Mathematics

Boris Khots
Observability and Mathematics Book PDF

Author : Boris Khots
Publisher : Advances in Applied Mathematics
Page : 214 pages
File Size : 53,6 Mb
Release : 2021-11-22
Category : Electronic
ISBN : 103200813X

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Observability and Mathematics by Boris Khots Pdf

The author approaches an old classic problem - the existence of solutions of Navier-Stokes equations. The main objective is to model and derive of equation of continuity, Euler equation of fluid motion, energy flux equation, Navier-Stokes equations from the observer point of view and solve classic problem for this interpretation of fluid motion laws. If we have a piece of metal or a volume of liquid, the idea impresses itself upon us that it is divisible without limit, that any part of it, however small, would again have the same properties. But, wherever the methods of research in the physics of matter were refined sufficiently, limits to divisibility were reached that are not due to the inadequacy of our experiments but to the nature of the subject matter. Observability in mathematics were developed by the author based on denial of infinity idea. He introduces observers into arithmetic, and arithmetic becomes dependent on observers. And after that the basic mathematical parts also become dependent on observers. This approach permits to reconsider the fluid motion laws, analyze them and get solutions of classic problems. Table of Contents 1. Introduction. 2. Observability and Arithmetic. 3. Observability and Vector Algebra. 4. Observability and Mathematical Analysis (Calculus). 5. Classic Fluid Mechanics equations and Observability. 6. Observability and Thermodynamical equations. 7. Observability and equation of continuity. 8. Observability and Euler equation of motion of the fluid. 9. Observability and energy flux and moment flux equations. 10. Observability and incompressible fluids. 11. Observability and Navier-Stokes equations. 12. Observability and Relativistic Fluid Mechanics. 13. Appendix: Review of publications of the Mathematics with Observers. 14. Glossary. Bibliography Index Biography Boris Khots, DrSci, lives in Iowa, USA, Independent Researcher. Alma Mater - Moscow State Lomonosov University, Department of Mathematics and Mechanics (mech-math). Creator of Observer's Mathematics. Participant of more than 30 Mathematical international congresses, conferences. In particular, participated with presentation at International Congresses of Mathematicians on 1998 (Germany), 2002 (China), 2006 (Spain), 2010 (India), 2014 (South Korea). More than 150 mathematical books and papers.

Mathematical Theory of Compressible Viscous Fluids

Eduard Feireisl,Trygve G. Karper,Milan Pokorný
Mathematical Theory of Compressible Viscous Fluids Book PDF

Author : Eduard Feireisl,Trygve G. Karper,Milan Pokorný
Publisher : Birkhäuser
Page : 186 pages
File Size : 47,9 Mb
Release : 2016-11-25
Category : Mathematics
ISBN : 9783319448350

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Mathematical Theory of Compressible Viscous Fluids by Eduard Feireisl,Trygve G. Karper,Milan Pokorný Pdf

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.

Three-Dimensional Navier-Stokes Equations for Turbulence

Luigi C. Berselli
Three Dimensional Navier Stokes Equations for Turbulence Book PDF

Author : Luigi C. Berselli
Publisher : Academic Press
Page : 330 pages
File Size : 53,5 Mb
Release : 2021-03-10
Category : Science
ISBN : 9780128219454

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Three-Dimensional Navier-Stokes Equations for Turbulence by Luigi C. Berselli Pdf

Three-Dimensional Navier-Stokes Equations for Turbulence provides a rigorous but still accessible account of research into local and global energy dissipation, with particular emphasis on turbulence modeling. The mathematical detail is combined with coverage of physical terms such as energy balance and turbulence to make sure the reader is always in touch with the physical context. All important recent advancements in the analysis of the equations, such as rigorous bounds on structure functions and energy transfer rates in weak solutions, are addressed, and connections are made to numerical methods with many practical applications. The book is written to make this subject accessible to a range of readers, carefully tackling interdisciplinary topics where the combination of theory, numerics, and modeling can be a challenge. Includes a comprehensive survey of modern reduced-order models, including ones for data assimilation Includes a self-contained coverage of mathematical analysis of fluid flows, which will act as an ideal introduction to the book for readers without mathematical backgrounds Presents methods and techniques in a practical way so they can be rapidly applied to the reader’s own work

Navier–Stokes Equations

Roger Temam
Navier Stokes Equations Book PDF

Author : Roger Temam
Publisher : American Mathematical Society
Page : 426 pages
File Size : 41,8 Mb
Release : 2024-05-24
Category : Mathematics
ISBN : 9781470477868

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Navier–Stokes Equations by Roger Temam Pdf

Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible. The new material in the present book (as compared to the preceding 1984 edition) is an appendix reproducing a survey article written in 1998. This appendix touches upon a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations. The book is written in the style of a textbook and the author has attempted to make the treatment self-contained. It can be used as a textbook or a reference book for researchers. Prerequisites for reading the book include some familiarity with the Navier-Stokes equations and some knowledge of functional analysis and Sololev spaces.

Analysis of the Navier-Stokes Problem

Alexander G. Ramm
Analysis of the Navier Stokes Problem Book PDF

Author : Alexander G. Ramm
Publisher : Unknown
Page : 0 pages
File Size : 53,9 Mb
Release : 2023
Category : Mathematical logic
ISBN : 3031307259

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Analysis of the Navier-Stokes Problem by Alexander G. Ramm Pdf

This book revises and expands upon the prior edition, The Navier-Stokes Problem. The focus of this book is to provide a mathematical analysis of the Navier-Stokes Problem (NSP) in R^3 without boundaries. Before delving into analysis, the author begins by explaining the background and history of the Navier-Stokes Problem. This edition includes new analysis and an a priori estimate of the solution. The estimate proves the contradictory nature of the Navier-Stokes Problem. The author reaches the conclusion that the solution to the NSP with smooth and rapidly decaying data cannot exist for all positive times. By proving the NSP paradox, this book provides a solution to the millennium problem concerning the Navier-Stokes Equations and shows that they are physically and mathematically contradictive. In addition, this book: Explains the background and history of the Navier-Stokes Problem Provides mathematical analysis of the Navier-Stokes Problem in R3 without boundaries Proves that the Navier-Stokes equations are physically and mathematically contradictive About the Author: Alexander G. Ramm, Ph.D., is a Professor Emeritus of Mathematics at Kansas State University. He is the author of approximately 715 research papers, 20 research monographs, and an editor of three books. Dr. Ramm won the Khwarizmi international award in 2004. His research interests include analysis, scattering theory, inverse problems, theoretical physics, engineering, signal estimation, tomography, theoretical numerical analysis, and applied mathematics.

Mathematical Analysis and Numerical Methods for Science and Technology

Robert Dautray,Jacques-Louis Lions
Mathematical Analysis and Numerical Methods for Science and Technology Book PDF

Author : Robert Dautray,Jacques-Louis Lions
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580048

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Mathematical Analysis and Numerical Methods for Science and Technology by Robert Dautray,Jacques-Louis Lions Pdf

These six volumes--the result of a ten year collaboration between two distinguished international figures--compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. It is a comprehensive and up-to-date publication that presents the mathematical tools needed in applications of mathematics.