Initial Boundary Value Problems And The Navier Stokes Equations

Author : Heinz-Otto Kreiss,Jens Lorenz
Publisher : SIAM
Page : 408 pages
File Size : 40,7 Mb
Release : 2004-01-01
Category : Science
ISBN : 9780898715651

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Initial-Boundary Value Problems and the Navier-Stokes Equation by Heinz-Otto Kreiss,Jens Lorenz Pdf

Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Applications to parabolic and hyperbolic systems are emphasized in this text. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. 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 book explains the principles of these subjects. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. Audience: when the book was written, the main intent was to write a text on initial-boundary value problems that was accessible to a rather wide audience. Functional analytical prerequisites were kept to a minimum or were developed in the book. Boundary conditions are analyzed without first proving trace theorems, and similar simplifications have been used throughout. This book continues to be useful to researchers and graduate students in applied mathematics and engineering.

Author : Jonas Nilsson
Publisher : Unknown
Page : 118 pages
File Size : 52,5 Mb
Release : 2000
Category : Boundary value problems
ISBN : 9155448852

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Initial-Boundary-Value Problems for the Stokes and Navier-Stokes Equations on Staggered Grids by Jonas Nilsson Pdf

Author : Wojciech M. Zajączkowski
Publisher : Unknown
Page : 44 pages
File Size : 45,6 Mb
Release : 1990
Category : Boundary value problems
ISBN : UCR:31210012616635

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On an Initial-boundary Value Problem for the Parabolic System which Appears in Free Boundary Problems for Compressible Navier-Stokes Equations by Wojciech M. Zajączkowski Pdf

Author : O. A. Ladyzhenskaya
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 46,7 Mb
Release : 1989
Category : Boundary value problems
ISBN : 0821831275

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Boundary Value Problems of Mathematical Physics by O. A. Ladyzhenskaya Pdf

Author : Gregory Seregin
Publisher : World Scientific
Page : 268 pages
File Size : 54,5 Mb
Release : 2014-09-16
Category : Mathematics
ISBN : 9789814623421

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Lecture Notes On Regularity Theory For The Navier-stokes Equations by Gregory Seregin Pdf

The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations.The global unique solvability (well-posedness) of initial boundary value problems for the Navier-Stokes equations is in fact one of the seven Millennium problems stated by the Clay Mathematical Institute in 2000. It has not been solved yet. However, a deep connection between regularity and well-posedness is known and can be used to attack the above challenging problem. This type of approach is not very well presented in the modern books on the mathematical theory of the Navier-Stokes equations. Together with introduction chapters, the lecture notes will be a self-contained account on the topic from the very basic stuff to the state-of-art in the field.

Author : S.N. Antontsev,A.V. Kazhiktov,V.N. Monakhov
Publisher : Elsevier
Page : 308 pages
File Size : 51,5 Mb
Release : 1989-12-18
Category : Mathematics
ISBN : 0080875432

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Boundary Value Problems in Mechanics of Nonhomogeneous Fluids by S.N. Antontsev,A.V. Kazhiktov,V.N. Monakhov Pdf

The objective of this book is to report the results of investigations made by the authors into certain hydrodynamical models with nonlinear systems of partial differential equations. The investigations involve the results concerning Navier-Stokes equations of viscous heat-conductive gas, incompressible nonhomogeneous fluid and filtration of multi-phase mixture in a porous medium. The correctness of the initial boundary-value problems and the qualitative properties of solutions are also considered. The book is written for those who are interested in the theory of nonlinear partial differential equations and their applications in mechanics.

Author : Olʹga A. Ladyženskaja
Publisher : American Mathematical Soc.
Page : 254 pages
File Size : 40,6 Mb
Release : 1991
Category : Boundary value problems
ISBN : 0821831410

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Boundary Value Problems of Mathematical Physics by Olʹga A. Ladyženskaja Pdf

Author : Giovanni Galdi
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 49,7 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.

Author : Giovanni P. Galdi,John G. Heywood,Rolf Rannacher
Publisher : Birkhäuser
Page : 300 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034884242

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Fundamental Directions in Mathematical Fluid Mechanics by Giovanni P. Galdi,John G. Heywood,Rolf Rannacher Pdf

This volume consists of six articles, each treating an important topic in the theory ofthe Navier-Stokes equations, at the research level. Some of the articles are mainly expository, putting together, in a unified setting, the results of recent research papers and conference lectures. Several other articles are devoted mainly to new results, but present them within a wider context and with a fuller exposition than is usual for journals. The plan to publish these articles as a book began with the lecture notes for the short courses of G.P. Galdi and R. Rannacher, given at the beginning of the International Workshop on Theoretical and Numerical Fluid Dynamics, held in Vancouver, Canada, July 27 to August 2, 1996. A renewed energy for this project came with the founding of the Journal of Mathematical Fluid Mechanics, by G.P. Galdi, J. Heywood, and R. Rannacher, in 1998. At that time it was decided that this volume should be published in association with the journal, and expanded to include articles by J. Heywood and W. Nagata, J. Heywood and M. Padula, and P. Gervasio, A. Quarteroni and F. Saleri. The original lecture notes were also revised and updated.

Author : John G. Heywood,Kyuya Masuda,Reimund Rautmann,Vsevolod A. Solonnikov
Publisher : Springer
Page : 245 pages
File Size : 55,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540471417

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The Navier-Stokes Equations Theory and Numerical Methods by John G. Heywood,Kyuya Masuda,Reimund Rautmann,Vsevolod A. Solonnikov Pdf

These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.

Author : Jerome Odell Sather
Publisher : Unknown
Page : 162 pages
File Size : 51,8 Mb
Release : 1963
Category : Boundary value problems
ISBN : MINN:31951T00413082Y

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The Initial-boundary Value Problem for the Navier-Stokes Equations in Regions with Moving Boundaries by Jerome Odell Sather Pdf

Author : Giovanni P. Galdi
Publisher : Unknown
Page : 480 pages
File Size : 40,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475738676

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An introduction to the mathematical theory of the Navier-Stokes equations by Giovanni P. Galdi Pdf

Author : John G. Heywood,Kyuya Masuda,Reimund Rautmann,Vsevolod A. Solonnikov
Publisher : Springer
Page : 329 pages
File Size : 48,5 Mb
Release : 2006-11-14
Category : Science
ISBN : 9783540474982

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The Navier-Stokes Equations II - Theory and Numerical Methods by John G. Heywood,Kyuya Masuda,Reimund Rautmann,Vsevolod A. Solonnikov Pdf

V.A. Solonnikov, A. Tani: Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid.- W. Borchers, T. Miyakawa:On some coercive estimates for the Stokes problem in unbounded domains.- R. Farwig, H. Sohr: An approach to resolvent estimates for the Stokes equations in L(q)-spaces.- R. Rannacher: On Chorin's projection method for the incompressible Navier-Stokes equations.- E. S}li, A. Ware: Analysis of the spectral Lagrange-Galerkin method for the Navier-Stokes equations.- G. Grubb: Initial value problems for the Navier-Stokes equations with Neumann conditions.- B.J. Schmitt, W. v.Wahl: Decomposition of solenoidal fields into poloidal fields, toroidal fields and the mean flow. Applications to the Boussinesq-equations.- O. Walsh: Eddy solutions of the Navier-Stokesequations.- W. Xie: On a three-norm inequality for the Stokes operator in nonsmooth domains.

Author : Giovanni P Galdi
Publisher : Springer
Page : 1034 pages
File Size : 51,9 Mb
Release : 2016-05-01
Category : Electronic
ISBN : 1493950177

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

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) "

Author : Giovanni Galdi
Publisher : Springer Science & Business Media
Page : 1026 pages
File Size : 53,5 Mb
Release : 2011-07-12
Category : Mathematics
ISBN : 9780387096209

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

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)