Mathematical Problems Relating To The Navier Stokes Equations

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

Author : Giovanni P Galdi
Publisher : Springer
ISBN 13 : 9781493950171
Total Pages : 1034 pages
Book Rating : 4.9/5 (51 download)

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Book Synopsis An Introduction to the Mathematical Theory of the Navier-Stokes Equations by : Giovanni P Galdi

Download or read book An Introduction to the Mathematical Theory of the Navier-Stokes Equations written by Giovanni P Galdi and published by Springer. This book was released on 2016-05-01 with total page 1034 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions in bounded as well as unbounded domains. Whenever the domain is unbounded, the asymptotic behavior of solutions is also investigated. This book is the new edition of the original two volume book, under the same title, published in 1994. In this new edition, the two volumes have merged into one and two more chapters on steady generalized oseen flow in exterior domains and steady Navier Stokes flow in three-dimensional exterior domains have been added. Most of the proofs given in the previous edition were also updated. An introductory first chapter describes all relevant questions treated in the book and lists and motivates a number of significant and still open questions. It is written in an expository style so as to be accessible also to non-specialists. Each chapter is preceded by a substantial, preliminary discussion of the problems treated, along with their motivation and the strategy used to solve them. Also, each chapter ends with a section dedicated to alternative approaches and procedures, as well as historical notes. The book contains more than 400 stimulating exercises, at different levels of difficulty, that will help the junior researcher and the graduate student to gradually become accustomed with the subject. Finally, the book is endowed with a vast bibliography that includes more than 500 items. Each item brings a reference to the section of the book where it is cited. The book will be useful to researchers and graduate students in mathematics in particular mathematical fluid mechanics and differential equations. Review of First Edition, First Volume: The emphasis of this book is on an introduction to the mathematical theory of the stationary Navier-Stokes equations. It is written in the style of a textbook and is essentially self-contained. The problems are presented clearly and in an accessible manner. Every chapter begins with a good introductory discussion of the problems considered, and ends with interesting notes on different approaches developed in the literature. Further, stimulating exercises are proposed. (Mathematical Reviews, 1995) "

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

Author : Franck Boyer
Publisher : Springer Science & Business Media
ISBN 13 : 1461459753
Total Pages : 538 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models by : Franck Boyer

Download or read book Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models written by Franck Boyer and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. .

Mathematical Problems Relating To The Navier-stokes Equations

Author : Giovanni Paolo Galdi
Publisher : World Scientific
ISBN 13 : 9814579823
Total Pages : 193 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Mathematical Problems Relating To The Navier-stokes Equations by : Giovanni Paolo Galdi

Download or read book Mathematical Problems Relating To The Navier-stokes Equations written by Giovanni Paolo Galdi and published by World Scientific. This book was released on 1992-08-14 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: A New Approach to the Helmholtz Decomposition and the Neumann Problem in Lq-Spaces for Bounded and Exterior Domains (C G Simader & H Sohr)On the Energy Equation and on the Uniqueness for D-Solutions to Steady Navier-Stokes Equations in Exterior Domains (G P Galdi)On the Asymptotic Structure of D-Solutions to Steady Navier-Stokes Equations in Exterior Domains (G P Galdi)On the Solvability of an Evolution Free Boundary Problem for the Navier-Stokes Equation in Hölder Spaces of Functions (I S Mogilevskii & V A Solonnikov) Readership: Applied mathematicians.

Mathematical Analysis of the Navier-Stokes Equations

Author : Matthias Hieber
Publisher : Springer Nature
ISBN 13 : 3030362264
Total Pages : 471 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Mathematical Analysis of the Navier-Stokes Equations by : Matthias Hieber

Download or read book Mathematical Analysis of the Navier-Stokes Equations written by Matthias Hieber and published by Springer Nature. This book was released on 2020-04-28 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Navier–Stokes Equations

Author : Grzegorz Łukaszewicz
Publisher : Springer
ISBN 13 : 331927760X
Total Pages : 395 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Navier–Stokes Equations by : Grzegorz Łukaszewicz

Download or read book Navier–Stokes Equations written by Grzegorz Łukaszewicz and published by Springer. This book was released on 2016-04-12 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from advanced undergraduate students to engineers and professional mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier–Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.

Lectures on Navier-Stokes Equations

Author : Tai-Peng Tsai
Publisher : American Mathematical Soc.
ISBN 13 : 1470430967
Total Pages : 239 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lectures on Navier-Stokes Equations by : Tai-Peng Tsai

Download or read book Lectures on Navier-Stokes Equations written by Tai-Peng Tsai and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a graduate text on the incompressible Navier-Stokes system, which is of fundamental importance in mathematical fluid mechanics as well as in engineering applications. The goal is to give a rapid exposition on the existence, uniqueness, and regularity of its solutions, with a focus on the regularity problem. To fit into a one-year course for students who have already mastered the basics of PDE theory, many auxiliary results have been described with references but without proofs, and several topics were omitted. Most chapters end with a selection of problems for the reader. After an introduction and a careful study of weak, strong, and mild solutions, the reader is introduced to partial regularity. The coverage of boundary value problems, self-similar solutions, the uniform L3 class including the celebrated Escauriaza-Seregin-Šverák Theorem, and axisymmetric flows in later chapters are unique features of this book that are less explored in other texts. The book can serve as a textbook for a course, as a self-study source for people who already know some PDE theory and wish to learn more about Navier-Stokes equations, or as a reference for some of the important recent developments in the area.

Initial-boundary Value Problems and the Navier-Stokes Equations

Author : Heinz-Otto Kreiss
Publisher : SIAM
ISBN 13 : 0898719135
Total Pages : 408 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Initial-boundary Value Problems and the Navier-Stokes Equations by : Heinz-Otto Kreiss

Download or read book Initial-boundary Value Problems and the Navier-Stokes Equations written by Heinz-Otto Kreiss and published by SIAM. This book was released on 1989-01-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.

Mathematical Problems of Statistical Hydromechanics

Author : M.I. Vishik
Publisher : Springer Science & Business Media
ISBN 13 : 9789027723369
Total Pages : 594 pages
Book Rating : 4.7/5 (233 download)

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Book Synopsis Mathematical Problems of Statistical Hydromechanics by : M.I. Vishik

Download or read book Mathematical Problems of Statistical Hydromechanics written by M.I. Vishik and published by Springer Science & Business Media. This book was released on 1988-05-31 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The ScandiJI of Father 'The Hermit Clad in Crane Feathers' in R. Brow" 'The point of a Pin'. van Gu\ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

The Navier-Stokes Equations

Author : Hermann Sohr
Publisher : Springer Science & Business Media
ISBN 13 : 3034805519
Total Pages : 376 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Navier-Stokes Equations by : Hermann Sohr

Download or read book The Navier-Stokes Equations written by Hermann Sohr and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.

Navier-stokes Equations In Planar Domains

Author : Matania Ben-artzi
Publisher : World Scientific
ISBN 13 : 1783263016
Total Pages : 315 pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Navier-stokes Equations In Planar Domains by : Matania Ben-artzi

Download or read book Navier-stokes Equations In Planar Domains written by Matania Ben-artzi and published by World Scientific. This book was released on 2013-03-07 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as “driven cavity” and “double-driven cavity”.A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a “pure streamfunction” approach. In particular, a complete proof of convergence is given for the full nonlinear problem.This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics./a

Compressible Navier-Stokes Equations

Author : Pavel Plotnikov
Publisher : Springer Science & Business Media
ISBN 13 : 3034803672
Total Pages : 470 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Compressible Navier-Stokes Equations by : Pavel Plotnikov

Download or read book Compressible Navier-Stokes Equations written by Pavel Plotnikov and published by Springer Science & Business Media. This book was released on 2012-08-04 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the modern state of the art in the mathematical theory of compressible Navier-Stokes equations, with particular emphasis on the applications to aerodynamics. The topics covered include: modeling of compressible viscous flows; modern mathematical theory of nonhomogeneous boundary value problems for viscous gas dynamics equations; applications to optimal shape design in aerodynamics; kinetic theory for equations with oscillating data; new approach to the boundary value problems for transport equations. The monograph offers a comprehensive and self-contained introduction to recent mathematical tools designed to handle the problems arising in the theory.

Applied Analysis of the Navier-Stokes Equations

Author : Charles R. Doering
Publisher : Cambridge University Press
ISBN 13 : 9780521445689
Total Pages : 236 pages
Book Rating : 4.4/5 (456 download)

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Book Synopsis Applied Analysis of the Navier-Stokes Equations by : Charles R. Doering

Download or read book Applied Analysis of the Navier-Stokes Equations written by Charles R. Doering and published by Cambridge University Press. This book was released on 1995 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Peter Constantin
Publisher : University of Chicago Press
ISBN 13 : 0226115496
Total Pages : 200 pages
Book Rating : 4.2/5 (261 download)

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Book Synopsis Navier-Stokes Equations by : Peter Constantin

Download or read book Navier-Stokes Equations written by Peter Constantin and published by University of Chicago Press. This book was released on 1988 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture notes of graduate courses given by the authors at Indiana University (1985-86) and the University of Chicago (1986-87). Paper edition, $14.95. Annotation copyright Book News, Inc. Portland, Or.

Navier—Stokes Equations and Related Nonlinear Problems

Author : Adélia Sequeira
Publisher : Springer Science & Business Media
ISBN 13 : 1489914153
Total Pages : 393 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Navier—Stokes Equations and Related Nonlinear Problems by : Adélia Sequeira

Download or read book Navier—Stokes Equations and Related Nonlinear Problems written by Adélia Sequeira and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the Third International Conference on Navier-Stokes Equations and Related Nonlinear Problems. The conference was held in Funchal (Madeira, Portugal), on May 21-27, 1994. In addition to the editor, the organizers were Carlos Albuquerque (FC, University of Lisbon), Casimiro Silva (University of Madeira) and Juha Videman (1ST, Technical University of Lisbon). This meeting, following two other successful events of similar type held in Thurnau (Germany) in 1992 and in Cento (Italy) in 1993, brought together, to the majestically beautiful island of Madeira, more than 60 specialists from all around the world, of which about two thirds were invited lecturers. The main interest of the meeting was focused on the mathematical analysis of nonlinear phenomena in fluid mechanics. During the conference, we noticed that this area seems to provide, today more than ever, challenging and increasingly important problems motivating the research of both theoretical and numerical analysts. This volume collects 32 articles selected from the invited lectures and contributed papers given during the conference. The main topics covered include: Flows in Unbounded Domains; Flows in Bounded Domains; Compressible Fluids; Free Boundary Problems; Non-Newtonian Fluids; Related Problems and Numerical Approximations. The contributions present original results or new surveys on recent developments, giving directions for future research. I express my gratitude to all the authors and I am glad to recognize the scientific level and the actual interest of the articles.

Navier-Stokes Equations and Turbulence

Author : C. Foias
Publisher : Cambridge University Press
ISBN 13 : 1139428993
Total Pages : 363 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Navier-Stokes Equations and Turbulence by : C. Foias

Download or read book Navier-Stokes Equations and Turbulence written by C. Foias and published by Cambridge University Press. This book was released on 2001-08-27 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience.

Navier-Stokes Equations

Author : Roger Temam
Publisher : American Mathematical Soc.
ISBN 13 : 0821827375
Total Pages : 426 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Navier-Stokes Equations by : Roger Temam

Download or read book Navier-Stokes Equations written by Roger Temam and published by American Mathematical Soc.. This book was released on 2001-04-10 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Navier-Stokes Equations and Related Nonlinear Problems

Author : H. Amann
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311231929X
Total Pages : 448 pages
Book Rating : 4.1/5 (123 download)

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Book Synopsis Navier-Stokes Equations and Related Nonlinear Problems by : H. Amann

Download or read book Navier-Stokes Equations and Related Nonlinear Problems written by H. Amann and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Navier-Stokes Equations and Related Nonlinear Problems".