The Stokes and Navier–Stokes Equations in Exterior Domains PDF Download

Author: David Wegmann
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832548394
Category : Juvenile Nonfiction
Languages : en
Pages : 131

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Book Description
In the first part of this thesis we established a maximal regularity result to the Stokes equations in exterior domains with moving boundary. This leads to existence of solutions to the Navier–Stokes equations globally in time for small data. Secondly, we consider Leray's problem on the decay of weak solutions to the Navier–Stokes equations in an exterior domain with non-homogeneous Dirichlet boundary data. It is shown that the solution decays polynomially.

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: Werner Varnhorn
Publisher: De Gruyter Akademie Forschung
ISBN:
Category : Mathematics
Languages : en
Pages : 176

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Book Description
The present book consists of three parts. In the first part a theory of solvability for the stationary Stokes equations in exterior domains is developed. We prove existence of strong solutions in Sobolev spaces and use a localisation principle and the divergence equation to deduce further properties of the solution (uniqueness, asymptotics).

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.

Author: Giovanni P Galdi
Publisher: Springer
ISBN: 9781493950171
Category :
Languages : en
Pages : 1034

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Book Description
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 Paolo Galdi
Publisher: World Scientific
ISBN: 9814579823
Category :
Languages : en
Pages : 193

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Book Description
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.

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: Giovanni Galdi
Publisher: Springer Science & Business Media
ISBN: 0387096205
Category : Mathematics
Languages : en
Pages : 1026

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Book Description
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: John G. Heywood
Publisher: Springer
ISBN: 3540474986
Category : Science
Languages : en
Pages : 329

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Book Description
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: L. Stupelis
Publisher: Springer Science & Business Media
ISBN: 9401585253
Category : Science
Languages : en
Pages : 583

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Book Description
The analytical basis of Navier-Stokes Equations in Irregular Domains is formed by coercive estimates, which enable proofs to be given of the solvability of the boundary value problems for Stokes and Navier-Stokes equations in weighted Sobolev and Hölder spaces, and the investigation of the smoothness of their solutions. This allows one to deal with the special problems that arise in the presence of edges or angular points in the plane case, at the boundary or noncompact boundaries. Such problems cannot be dealt with in any of the usual ways. Audience: Graduate students, research mathematicians and hydromechanicians whose work involves functional analysis and its applications to Navier-Stokes equations.