The Steady Navier Stokes System

Author : Tujin Kim,Daomin Cao
Publisher : Springer Nature
Page : 374 pages
File Size : 54,9 Mb
Release : 2021-09-09
Category : Mathematics
ISBN : 9783030786595

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Equations of Motion for Incompressible Viscous Fluids by Tujin Kim,Daomin Cao Pdf

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 : Mikhail Korobkov,Konstantin Pileckas,Remigio Russo
Publisher : Birkhäuser
Page : 0 pages
File Size : 52,5 Mb
Release : 2024-05-12
Category : Mathematics
ISBN : 3031508971

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The Steady Navier-Stokes System by Mikhail Korobkov,Konstantin Pileckas,Remigio Russo Pdf

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 : Mikhail Korobkov
Publisher : Springer Nature
Page : 296 pages
File Size : 47,5 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9783031508981

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The Steady Navier-Stokes System by Mikhail Korobkov Pdf

Author : Giovanni Galdi
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 53,6 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 : Matania Ben-artzi,Jean Pierre Croisille,Dalia Fishelov
Publisher : World Scientific
Page : 316 pages
File Size : 51,5 Mb
Release : 2013-03-07
Category : Mathematics
ISBN : 9781783263011

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Navier-stokes Equations In Planar Domains by Matania Ben-artzi,Jean Pierre Croisille,Dalia Fishelov Pdf

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 : Roger Temam
Publisher : American Mathematical Soc.
Page : 426 pages
File Size : 51,6 Mb
Release : 2001-04-10
Category : Mathematics
ISBN : 9780821827376

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Navier-Stokes Equations by Roger Temam Pdf

Originally published in 1977, the book is devoted to the theory and numerical analysis of the Navier-Stokes equations for viscous incompressible fluid. On the theoretical side, results related to the existence, the uniqueness, and, in some cases, the regularity of solutions are presented. On the numerical side, various approaches to the approximation of Navier-Stokes problems by discretization are considered, such as the finite dereference method, the finite element method, and the fractional steps method. The problems of stability and convergence for numerical methods are treated as completely as possible. The new material in the present book (as compared to the preceding 1984 edition) is an appendix reproducing a survey article written in 1998. This appendix touches upon a few aspects not addressed in the earlier editions, in particular a short derivation of the Navier-Stokes equations from the basic conservation principles in continuum mechanics, further historical perspectives, and indications on new developments in the area. The appendix also surveys some aspects of the related Euler equations and the compressible Navier-Stokes equations. The book is written in the style of a textbook and the author has attempted to make the treatment self-contained. It can be used as a textbook or a reference book for researchers. Prerequisites for reading the book include some familiarity with the Navier-Stokes equations and some knowledge of functional analysis and Sololev spaces.

Author : Tai-Peng Tsai
Publisher : American Mathematical Soc.
Page : 224 pages
File Size : 51,6 Mb
Release : 2018-08-09
Category : Fluid dynamics
ISBN : 9781470430962

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Lectures on Navier-Stokes Equations by Tai-Peng Tsai Pdf

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 : Viorel Barbu,Irena Lasiecka,Roberto Triggiani
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 46,8 Mb
Release : 2006
Category : Boundary layer
ISBN : 9780821838747

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Tangential Boundary Stabilization of Navier-Stokes Equations by Viorel Barbu,Irena Lasiecka,Roberto Triggiani Pdf

In order to inject dissipation as to force local exponential stabilization of the steady-state solutions, an Optimal Control Problem (OCP) with a quadratic cost functional over an infinite time-horizon is introduced for the linearized N-S equations. As a result, the same Riccati-based, optimal boundary feedback controller which is obtained in the linearized OCP is then selected and implemented also on the full N-S system. For $d=3$, the OCP falls definitely outside the boundaries of established optimal control theory for parabolic systems with boundary controls, in that the combined index of unboundedness--between the unboundedness of the boundary control operator and the unboundedness of the penalization or observation operator--is strictly larger than $\tfrac{3}{2}$, as expressed in terms of fractional powers of the free-dynamics operator. In contrast, established (and rich) optimal control theory [L-T.2] of boundary control parabolic problems and corresponding algebraic Riccati theory requires a combined index of unboundedness strictly less than 1. An additional preliminary serious difficulty to overcome lies at the outset of the program, in establishing that the present highly non-standard OCP--with the aforementioned high level of unboundedness in control and observation operators and subject, moreover, to the additional constraint that the controllers be pointwise tangential--be non-empty; that is, it satisfies the so-called Finite Cost Condition [L-T.2].

Author : Adélia Sequeira
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 49,7 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781489914156

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Navier—Stokes Equations and Related Nonlinear Problems by Adélia Sequeira Pdf

This volume contains the Proceedings of the Third International Conference on Navier-Stokes Equations and Related Nonlinear Problems. The conference was held in Funchal (Madeira, Portugal), on May 21-27, 1994. In addition to the editor, the organizers were Carlos Albuquerque (FC, University of Lisbon), Casimiro Silva (University of Madeira) and Juha Videman (1ST, Technical University of Lisbon). This meeting, following two other successful events of similar type held in Thurnau (Germany) in 1992 and in Cento (Italy) in 1993, brought together, to the majestically beautiful island of Madeira, more than 60 specialists from all around the world, of which about two thirds were invited lecturers. The main interest of the meeting was focused on the mathematical analysis of nonlinear phenomena in fluid mechanics. During the conference, we noticed that this area seems to provide, today more than ever, challenging and increasingly important problems motivating the research of both theoretical and numerical analysts. This volume collects 32 articles selected from the invited lectures and contributed papers given during the conference. The main topics covered include: Flows in Unbounded Domains; Flows in Bounded Domains; Compressible Fluids; Free Boundary Problems; Non-Newtonian Fluids; Related Problems and Numerical Approximations. The contributions present original results or new surveys on recent developments, giving directions for future research. I express my gratitude to all the authors and I am glad to recognize the scientific level and the actual interest of the articles.

Author : Luigi C. Berselli
Publisher : Academic Press
Page : 330 pages
File Size : 50,6 Mb
Release : 2021-03-10
Category : Science
ISBN : 9780128219454

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Three-Dimensional Navier-Stokes Equations for Turbulence by Luigi C. Berselli Pdf

Three-Dimensional Navier-Stokes Equations for Turbulence provides a rigorous but still accessible account of research into local and global energy dissipation, with particular emphasis on turbulence modeling. The mathematical detail is combined with coverage of physical terms such as energy balance and turbulence to make sure the reader is always in touch with the physical context. All important recent advancements in the analysis of the equations, such as rigorous bounds on structure functions and energy transfer rates in weak solutions, are addressed, and connections are made to numerical methods with many practical applications. The book is written to make this subject accessible to a range of readers, carefully tackling interdisciplinary topics where the combination of theory, numerics, and modeling can be a challenge. Includes a comprehensive survey of modern reduced-order models, including ones for data assimilation Includes a self-contained coverage of mathematical analysis of fluid flows, which will act as an ideal introduction to the book for readers without mathematical backgrounds Presents methods and techniques in a practical way so they can be rapidly applied to the reader’s own work

Author : P. G. Drazin,N. Riley
Publisher : Cambridge University Press
Page : 212 pages
File Size : 50,6 Mb
Release : 2006-05-25
Category : Mathematics
ISBN : 0521681626

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The Navier-Stokes Equations by P. G. Drazin,N. Riley Pdf

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

Author : H. Amann,G . P. Galdi,K. Plleckas,V. A. Solonnikov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 448 pages
File Size : 55,6 Mb
Release : 2020-05-18
Category : Mathematics
ISBN : 9783112319291

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Navier-Stokes Equations and Related Nonlinear Problems by H. Amann,G . P. Galdi,K. Plleckas,V. A. Solonnikov Pdf

No detailed description available for "Navier-Stokes Equations and Related Nonlinear Problems".

Author : John Groves Heywood
Publisher : World Scientific
Page : 256 pages
File Size : 55,9 Mb
Release : 1998
Category : Mathematics
ISBN : 9810233000

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Theory of the Navier-Stokes Equations by John Groves Heywood Pdf

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 : Vasiliĭ Sergeevich Vladimirov,Evgeniĭ Frolovich Mishchenko,A. K. Gushchin
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 53,8 Mb
Release : 1988
Category : Mathematics
ISBN : 0821831194

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Theoretical and Mathematical Physics by Vasiliĭ Sergeevich Vladimirov,Evgeniĭ Frolovich Mishchenko,A. K. Gushchin Pdf

Author : Giovanni Galdi
Publisher : Springer Science & Business Media
Page : 1026 pages
File Size : 49,6 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)