Author: Mikhail Korobkov
Publisher: Springer Nature
ISBN: 303150898X
Category : Differential equations
Languages : en
Pages : 296
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Book Description
Zusammenfassung: This book provides a successful solution to one of the central problems of mathematical fluid mechanics: the Leray's problem on existence of a solution to the boundary value problem for the stationary Navier--Stokes system in bounded domains under sole condition of zero total flux. This marks the culmination of the authors' work over the past few years on this under-explored topic within the study of the Navier--Stokes equations. This book will be the first major work on the Navier--Stokes equations to explore Leray's problem in detail. The results are presented with detailed proofs, as are the history of the problem and the previous approaches to finding a solution to it. In addition, for the reader's convenience and for the self-sufficiency of the text, the foundations of the mathematical theory for incompressible fluid flows described by the steady state Stokes and Navier--Stokes systems are presented. For researchers in this active area, this book will be a valuable resource
Author: Tujin Kim
Publisher: Springer Nature
ISBN: 3030786595
Category : Mathematics
Languages : en
Pages : 374
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Book Description
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: Tai-Peng Tsai
Publisher: American Mathematical Soc.
ISBN: 1470430967
Category : Mathematics
Languages : en
Pages : 239
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Book Description
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.
Author: Matania Ben-artzi
Publisher: World Scientific
ISBN: 1783263016
Category : Mathematics
Languages : en
Pages : 315
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Book Description
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
Author: John Groves Heywood
Publisher: World Scientific
ISBN: 9789810233006
Category : Mathematics
Languages : en
Pages : 256
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Book Description
This volume collects the articles presented at the Third International Conference on ?The Navier-Stokes Equations: Theory and Numerical Methods?, held in Oberwolfach, Germany. The articles are important contributions to a wide variety of topics in the Navier-Stokes theory: general boundary conditions, flow exterior to an obstacle, conical boundary points, the controllability of solutions, compressible flow, non-Newtonian flow, magneto-hydrodynamics, thermal convection, the interaction of fluids with elastic solids, the regularity of solutions, and Rothe's method of approximation.
Author: P. G. Drazin
Publisher: Cambridge University Press
ISBN: 9780521681629
Category : Mathematics
Languages : en
Pages : 212
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Book Description
This 2006 book details exact solutions to the Navier-Stokes equations for senior undergraduates and graduates or research reference.
Author: Chi-Sing Man
Publisher: Springer Science & Business Media
ISBN: 1402023081
Category : Science
Languages : en
Pages : 828
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Book Description
Through his voluminous and in?uential writings, editorial activities, organi- tional leadership, intellectual acumen, and strong sense of history, Clifford - brose Truesdell III (1919–2000) was the main architect for the renaissance of - tional continuum mechanics since the middle of the twentieth century. The present collection of 42 essays and research papers pays tribute to this man of mathematics, science, and natural philosophy as well as to his legacy. The ?rst ?ve essays by B. D. Coleman, E. Giusti, W. Noll, J. Serrin, and D. Speiser were texts of addresses given by their authors at the Meeting in memory of Clifford Truesdell, which was held in Pisa in November 2000. In these essays the reader will ?nd personal reminiscences of Clifford Truesdell the man and of some of his activities as scientist, author, editor, historian of exact sciences, and principal founding member of the Society for Natural Philosophy. The bulk of the collection comprises 37 research papers which bear witness to the Truesdellian legacy. These papers cover a wide range of topics; what ties them together is the rational spirit. Clifford Truesdell, in his address upon receipt of a Birkhoff Prize in 1978, put the essence of modern continuum mechanics succinctly as “conceptual analysis, analysis not in the sense of the technical term but in the root meaning: logical criticism, dissection, and creative scrutiny.
Author: Björn Engquist
Publisher: Springer
ISBN: 364256478X
Category : Mathematics
Languages : en
Pages : 1219
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Book Description
This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.
Author: George Gabriel 1819-1903 Stokes
Publisher: Legare Street Press
ISBN: 9781015199002
Category :
Languages : en
Pages : 104
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Book Description
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author: Hermann Sohr
Publisher: Springer Science & Business Media
ISBN: 3034805519
Category : Mathematics
Languages : en
Pages : 376
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Book Description
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.
