An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Volume II: Nonlinear Steady Problems de Giovanni Galdi

An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Volume II: Nonlinear Steady Problems: Springer Tracts in Natural Philosophy, cartea 39

Autor Giovanni Galdi

en Limba Engleză Paperback – 12 oct 2011

This is the second of four volumes on the Navier-Stokes equations, specifically on Nonlinear Stationary Problems. The volumes deal with the fundamental mathematical properties of the Navier-Stokes equations, such as existence, regularity and uniqueness of solutions, and, for unbounded domains, their asymptotic behavior. The work is an up-to-date and detailed investigation of these problems for motions in domains of different types: bounded, exterior and domain with noncompact boundaries. Throughout the work, main problems which, so far, remain open are pointed out and for some of these conjectures are offered. New results are presented throughout, while several classical subjects are treated in a completely original way. The work is mathematically self contained, requiring no specific background. The 200-plus exercises along with the chapter summaries and questions make this an excellent textbook for any theoretical Fluid Mechanics course; it is suitable as well for self teaching. It is set up to remain useful as a reference or dictionary.

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Specificații

ISBN-13: 9781461253662
ISBN-10: 1461253667
Pagini: 360
Ilustrații: XIII, 364 p.
Dimensiuni: 155 x 235 x 19 mm
Greutate: 0.51 kg
Ediția:Softcover reprint of the original 1st ed. 1994
Editura: Springer
Colecția Springer
Seria Springer Tracts in Natural Philosophy

Locul publicării:New York, NY, United States

Public țintă

Graduate

Cuprins

VIII Steady Navier-Stokes Flow in Bounded Domains.- VIII. 1 Generalised Solutions. Preliminary Considerations.- VIII.2 On the Uniqueness of Generalised Solutions.- VIII.3 Existence and Uniqueness with Homogeneous Boundary Data.- VIII.4 Existence and Uniqueness with Nonhomogeneous Boundary Data.- VIII.5 Regularity of Generalised Solutions.- VIII.6 Limit of Infinite Viscosity: Transition to the Stokes Problem.- VIII. 7 Notes for the Chapter.- IX Steady Navier-Stokes Flow in Three-Dimensional Exterior Domains.- IX.1 Generalised Solutions. Preliminary Considerations and Regularity Properties.- IX.2 On the Validity of the Energy Equation for Generalised Solutions.- IX.3 Some Uniqueness Results.- IX.4 Existence of Generalised Solutions.- IX.5 The Energy Equation and Uniqueness for Generalised Solutions when ?? ? 0.- IX.6 On the Asymptotic Behaviour of Generalised Solutions: Preliminary Results and Representation Formulas.- IX.7 Global Summability of Generalised Solutions when ?? ? 0.- IX.8 The Asymptotic Structure of Generalised Solutions when ?? ? 0.- IX.9 On the Asymptotic Structure of Generalised Solutions when ?? ? 0.- IX. 10 Limit of Vanishing Reynolds Number: Transition to the Stokes Problem.- IX. 11 Notes for the Chapter.- X Steady Navier-Stokes Flow in Two-Dimensional Exterior Domains.- X.1 Generalised Solutions and D-Solutions.- X.2 On the Uniqueness of Generalised Solutions.- X.3 On the Asymptotic Behaviour of D-Solutions.- X.4 Existence and Uniqueness of Solutions when ?? ? 0.- X.5 Global Summability of Generalised Solutions when ?? ? 0.- X.6 The Asymptotic Structure of Generalised Solutions when ?? ? 0.- X.7 Limit of Vanishing Reynolds Number: Transition to the Stokes Problem.- X.8 Notes for the Chapter.- XI Steady Navier-StokesFlow in Domains with Unbounded Boundaries.- XI.1 Leray’s Problem: Generalised Solutions and Related Properties.- XI.2 On the Uniqueness of Generalised Solutions to Leray’s Problem.- XI.3 Existence and Uniqueness of Solutions to Leray’s Problem.- XI.4 Decay Estimates for Steady Flow in a Semi-Infinite Straight Channel.- XI.5 Flow in an Aperture Domain. Generalised Solutions and Related Properties.- XI.6 Energy Equation and Uniqueness for Flows in an Aperture Domain.- XI.7 Existence and Uniqueness of Flows in an Aperture Domain.- XI.8 Global Summability of Generalised Solutions for Flow in an Aperture Domain.- XI.9 Asymptotic Structure of Generalised Solutions for Flow in an Aperture Domain.- XI. 10 Notes for the Chapter.

Recenzii

From the reviews of the second edition:
“The book yields a comprehensive, detailed and self-contained study of the basic mathematical properties of different boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions. … The book contains more than 400 carefully choosen exercises at different levels of difficulty that will help the young researcher. The comprehensive bibliography contains more than 500 items. Galdi’s monograph can strongly be recommended to every mathematician (and theoretical physicist) interested in mathematical fluid mechanics or in PDEs.” (Jürgen Socolowsky, Zentralblatt MATH, Vol. 1245, 2012)

Textul de pe ultima copertă

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 themathematical 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)

Caracteristici

Chapter and summary sections included. Exercises at the ends of the chapters Two new chapters have been added Includes supplementary material: sn.pub/extras