The Three-Dimensional Navier–Stokes Equations

Classical Theory

Author: James C. Robinson,José L. Rodrigo,Witold Sadowski

Publisher: Cambridge University Press

ISBN: 1316715124

Category: Mathematics

Page: N.A

View: 5035

A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier–Stokes equations, this book provides self-contained proofs of some of the most significant results in the area, many of which can only be found in research papers. Highlights include the existence of global-in-time Leray–Hopf weak solutions and the local existence of strong solutions; the conditional local regularity results of Serrin and others; and the partial regularity results of Caffarelli, Kohn, and Nirenberg. Appendices provide background material and proofs of some 'standard results' that are hard to find in the literature. A substantial number of exercises are included, with full solutions given at the end of the book. As the only introductory text on the topic to treat all of the mainstream results in detail, this book is an ideal text for a graduate course of one or two semesters. It is also a useful resource for anyone working in mathematical fluid dynamics.
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Lectures on Navier-Stokes Equations

Author: Tai-Peng Tsai

Publisher: American Mathematical Soc.

ISBN: 1470430967

Category: Fluid dynamics

Page: 224

View: 9072

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.
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Partial Differential Equations in Fluid Mechanics

Author: Charles L. Fefferman,James C. Robinson,José L. Rodrigo

Publisher: Cambridge University Press

ISBN: 1108460968

Category: Mathematics

Page: 336

View: 7494

A selection of survey articles and original research papers in mathematical fluid mechanics, for both researchers and graduate students.
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A Course in Finite Group Representation Theory

Author: Peter Webb

Publisher: Cambridge University Press

ISBN: 131678536X

Category: Mathematics

Page: N.A

View: 874

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
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The Navier-Stokes Equations

A Classification of Flows and Exact Solutions

Author: P. G. Drazin,N. Riley

Publisher: Cambridge University Press

ISBN: 9780521681629

Category: Mathematics

Page: 196

View: 6781

This 2006 book details exact solutions to the Navier-Stokes equations for senior undergraduates and graduates or research reference.
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Physics Briefs

Physikalische Berichte

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Physics

Page: N.A

View: 6195

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Science Abstracts

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Physics

Page: N.A

View: 4322

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Vortex Methods

Theory and Practice

Author: Georges-Henri Cottet,Petros D. Koumoutsakos

Publisher: Cambridge University Press

ISBN: 0521621860

Category: Mathematics

Page: 313

View: 6623

Vortex methods have matured in recent years, offering an interesting alternative to finite difference and spectral methods for high resolution numerical solutions of the Navier Stokes equations. In the past three decades, research into the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character, which was the motivation for their introduction. This book presents and analyzes vortex methods as a tool for the direct numerical simulation of impressible viscous flows. It will interest graduate students and researchers in numerical analysis and fluid mechanics and also serve as an ideal textbook for courses in fluid dynamics.
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NASA SP.

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Aeronautics

Page: N.A

View: 548

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Nonlinear Evolutionary Partial Differential Equations

International Conference on Nonlinear Evolutionary Partial Differential Equations, June 21-25, 1993, Beijing, People's Republic of China

Author: Xiaxi Ding,Tai-Ping Liu

Publisher: American Mathematical Soc.

ISBN: 0821806610

Category: Mathematics

Page: 637

View: 4393

This volume contains the proceedings from the International Conference on Nonlinear Evolutionary Partial Differential Equations held in Beijing in June 1993. The topic for the conference was selected because of its importance in the natural sciences and for its mathematical significance. Discussion topics include conservation laws, dispersion waves, Einstein's theory of gravitation, reaction-diffusion equations, the Navier-Stokes equations, and more. New results were presented and are featured in this volume. Titles in this series are co-published with International Press, Cambridge, MA.
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Fast Solvers for Flow Problems

Proceedings of the Tenth GAMM-Seminar Kiel, January 14–16, 1994

Author: Wolfgang Hackbusch,Gabriel Wittum

Publisher: Springer-Verlag

ISBN: 366314125X

Category: Science

Page: 292

View: 5673

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Theory and Computation of Hydrodynamic Stability

Author: W. O. Criminale,T. L. Jackson,Ronald Douglas Joslin

Publisher: Cambridge University Press

ISBN: 9780521632003

Category: Mathematics

Page: 441

View: 4013

Graduate text/reference with exercises, computer code on basic topic in fluid dynamics.
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Differentialgleichungen und ihre Anwendungen

Author: Martin Braun

Publisher: Springer-Verlag

ISBN: 3642973418

Category: Mathematics

Page: 596

View: 9644

Dieses richtungsweisende Lehrbuch für die Anwendung der Mathematik in anderen Wissenschaftszweigen gibt eine Einführung in die Theorie der gewöhnlichen Differentialgleichungen. Fortran und APL-Programme geben den Studenten die Möglichkeit, verschiedene numerische Näherungsverfahren an ihrem PC selbst durchzurechnen. Aus den Besprechungen: "Die Darstellung ist überall mathematisch streng und zudem ungemein anregend. Abgesehen von manchen historischen Bemerkungen ... tragen dazu die vielen mit ausführlichem Hintergrund sehr eingehend entwickelten praktischen Anwendungen bei. ... Besondere Aufmerksamkeit wird der physikalisch und technisch so wichtigen Frage nach Stabilität von Lösungen eines Systems von Differentialgleichungen gewidmet. Das Buch ist wegen seiner geringen Voraussetzungen und vorzüglichen Didaktik schon für alle Studenten des 3. Semesters geeignet; seine eminent praktische Haltung empfiehlt es aber auch für alle Physiker, die mit Differentialgleichungen und ihren Anwendungen umzugehen haben." #Physikalische Blätter#
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Rarefied Gas Dynamics

From Basic Concepts to Actual Calculations

Author: Carlo Cercignani

Publisher: Cambridge University Press

ISBN: 9780521659925

Category: Mathematics

Page: 320

View: 5378

The aim of this book is to present the concepts, methods and applications of kinetic theory to rarefied gas dynamics. After introducing the basic tools, problems in plane geometry are treated using approximation techniques (perturbation and numerical methods). These same techniques are later used to deal with two- and three-dimensional problems. The models include not only monatomic but also polyatomic gases, mixtures, chemical reactions. A special chapter is devoted to evaporation and condensation phenomena. Each section is accompanied by problems which are mainly intended to demonstrate the use of the material in the text and to outline additional subjects, results and equations. This will help ensure that the book can be used for a range of graduate courses in aerospace engineering or applied mathematics.
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