Download or read book Quelques probl mes aux limites pour les quations de Navier Stokes written by Vincent Girinon and published by . This book was released on 2008 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cette thèse, composée de quatre chapitres, aborde sur quelques exemples le problème de l'existence de solutions aux équations de Navier-Stokes pour le modèle de l'écoulement isentropique d'un gaz parfait. Le premier chapitre regroupe les théorèmes classiques utilisés pour étudier les équations de Navier-Stokes. Nous y avons ajouté quelques résultats, spécifiquement développés pour ce travail, qui concernent l'équation de conservation de la masse. Dans le second chapitre, nous nous intéressons à un écoulement bidimensionnel entre deux parois parallèles. Le domaine sur lequel sont étudiées les équations est alors un rectangle et le système d'équations est complété par des conditions initiales et des conditions limites portant sur la densité et la vitesse du gaz. Nous fournissons alors une preuve de l'existence d'une solution à ce problème en nous appuyant sur une extension convenable des conditions de bord. Dans le troisième chapitre, en nous inspirant des idées exploitées au chapitre précédent, nous développons l'étude de deux nouveaux exemples. Le premier concerne un problème d'écoulement autour d'une aile d'avion et le second exemple reprend le modèle du chapitre deux en modifiant la vitesse sur le bord du domaine. Le quatrième et dernier chapitre traite de l'existence d'une solution aux équations de Navier-Stokes linéarisées au voisinage d'une solution stationnaire. Nous prouvons un tel résultat dans le cas d'un écoulement semblable à celui étudié au chapitre deux. Enfin, nous terminons ce chapitre en démontrant le caractère exponentiellement stable du système étudié dans le cas monodimensionnel.

Download or read book Navier Stokes Equations and Turbulence written by C. Foias and published by Cambridge University Press. This book was released on 2001-08-27 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience.

Download or read book Quelques m thodes de r solution des probl mes aux limites non lin aires written by Jacques-Louis Lions and published by . This book was released on 1969 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Compressible Navier Stokes Equations written by Pavel Plotnikov and published by Springer Science & Business Media. This book was released on 2012-08-04 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the modern state of the art in the mathematical theory of compressible Navier-Stokes equations, with particular emphasis on the applications to aerodynamics. The topics covered include: modeling of compressible viscous flows; modern mathematical theory of nonhomogeneous boundary value problems for viscous gas dynamics equations; applications to optimal shape design in aerodynamics; kinetic theory for equations with oscillating data; new approach to the boundary value problems for transport equations. The monograph offers a comprehensive and self-contained introduction to recent mathematical tools designed to handle the problems arising in the theory.

Download or read book Contributions to Current Challenges in Mathematical Fluid Mechanics written by Giovanni P. Galdi and published by Birkhäuser. This book was released on 2012-12-06 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of five research articles, each dedicated to a significant topic in the mathematical theory of the Navier-Stokes equations, for compressible and incompressible fluids, and to related questions. All results given here are new and represent a noticeable contribution to the subject. One of the most famous predictions of the Kolmogorov theory of turbulence is the so-called Kolmogorov-obukhov five-thirds law. As is known, this law is heuristic and, to date, there is no rigorous justification. The article of A. Biryuk deals with the Cauchy problem for a multi-dimensional Burgers equation with periodic boundary conditions. Estimates in suitable norms for the corresponding solutions are derived for "large" Reynolds numbers, and their relation with the Kolmogorov-Obukhov law are discussed. Similar estimates are also obtained for the Navier-Stokes equation. In the late sixties J. L. Lions introduced a "perturbation" of the Navier Stokes equations in which he added in the linear momentum equation the hyper dissipative term (-Ll),Bu, f3 ~ 5/4, where Ll is the Laplace operator. This term is referred to as an "artificial" viscosity. Even though it is not physically moti vated, artificial viscosity has proved a useful device in numerical simulations of the Navier-Stokes equations at high Reynolds numbers. The paper of of D. Chae and J. Lee investigates the global well-posedness of a modification of the Navier Stokes equation similar to that introduced by Lions, but where now the original dissipative term -Llu is replaced by (-Ll)O:u, 0 S Ct

Download or read book Navier Stokes Equations written by Roger Temam and published by American Mathematical Society. This book was released on 2024-05-24 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Finite Element Methods for Navier Stokes Equations written by Vivette Girault and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material covered by this book has been taught by one of the authors in a post-graduate course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an extended version of a previous text (cf. Girault & Raviart [32J) published in 1979 by Springer-Verlag in its series: Lecture Notes in Mathematics. In the last decade, many engineers and mathematicians have concentrated their efforts on the finite element solution of the Navier-Stokes equations for incompressible flows. The purpose of this book is to provide a fairly comprehen sive treatment of the most recent developments in that field. To stay within reasonable bounds, we have restricted ourselves to the case of stationary prob lems although the time-dependent problems are of fundamental importance. This topic is currently evolving rapidly and we feel that it deserves to be covered by another specialized monograph. We have tried, to the best of our ability, to present a fairly exhaustive treatment of the finite element methods for inner flows. On the other hand however, we have entirely left out the subject of exterior problems which involve radically different techniques, both from a theoretical and from a practical point of view. Also, we have neither discussed the implemen tation of the finite element methods presented by this book, nor given any explicit numerical result. This field is extensively covered by Peyret & Taylor [64J and Thomasset [82].

Download or read book Implementation of Finite Element Methods for Navier Stokes Equations written by F. Thomasset and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.

Download or read book Equations de Stokes et de Navier Stokes avec des conditions aux limites de Navier written by Ahmed Rejaiba and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Résumé : Cette thèse est consacrée à l'étude des équations de Stokes et de Navier-Stokes avec des conditions aux limites de Navier dans un ouvert borné de . Le manuscrit ici est composé de trois chapitres. Dans le premier, nous considérons les équations de Stokes stationnaires avec des conditions aux limites de Navier. Nous démontrons l'existence, l'unicité et la régularité de la solution d'abord dans un cadre hilbertien puis dans le cadre de la théorie . Nous traitons aussi le cas de solutions très faibles. Dans le deuxième chapitre, nous nous intéressons aux équations de Navier-Stokes avec la condition de Navier. Sous certaines hypothèses sur les données, nous démontrons l'existence de solution faible dans , avec en utilisant un théorème du point fixe appliqué à un problème d'Oseen. Nous démontrons examinons ensuite les questions de régularité des solutions en particulier dans . Dans le dernier chapitre, nous étudions le problème d'évolution de Stokes avec la condition de Navier. La résolution de ce problème se fait au moyen de la théorie des semi-groupes analytiques qui jouent un rôle important pour établir l'existence et l'unicité de la solution dans le cas homogène. Nous traitons le cas du problème non homogène par le biais des puissances imaginaires de l'opérateur de Stokes.

Download or read book Handbook of Differential Equations Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2008-10-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.- Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts

Download or read book Hydrodynamic Limits of the Boltzmann Equation written by Laure Saint-Raymond and published by Springer Science & Business Media. This book was released on 2009-03-26 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The material published in this volume comes essentially from a course given at the Conference on "Boltzmann equation and fluidodynamic limits", held in Trieste in June 2006." -- preface.

Download or read book Stability to the Incompressible Navier Stokes Equations written by Guilong Gui and published by Springer Science & Business Media. This book was released on 2013-04-13 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis contains results of Dr. Guilong Gui during his PhD period with the aim to understand incompressible Navier-Stokes equations. It is devoted to the study of the stability to the incompressible Navier-Stokes equations. There is great potential for further theoretical and numerical research in this field. The techniques developed in carrying out this work are expected to be useful for other physical model equations. It is also hopeful that the thesis could serve as a valuable reference on current developments in research topics related to the incompressible Navier-Stokes equations. It was nominated by the Graduate University of Chinese Academy of Sciences as an outstanding PhD thesis.​

Download or read book Nonlinear Functional Analysis and Its Applications Part 1 written by Felix E. Browder and published by American Mathematical Soc.. This book was released on 1986 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Mathematical Fluid Dynamics written by S. Friedlander and published by Elsevier. This book was released on 2002-07-09 with total page 829 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

Download or read book Mathematical Topics in Fluid Mechanics Volume 2 Compressible Models written by Pierre-Louis Lions and published by Oxford University Press. This book was released on 1996 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluid mechanics models consist of systems of nonlinear partial differential equations for which, despite a long history of important mathematical contributions, no complete mathematical understanding is available. The second volume of this book describes compressible fluid-mechanics models. The book contains entirely new material on a subject known to be rather difficult and important for applications (compressible flows). It is probably a unique effort on the mathematical problems associated with the compressible Navier-Stokes equations, written by one of the world's leading experts on nonlinear partial differential equations. Professor P.L. Lions won the Fields Medal in 1994.

Download or read book SUR LES EQUATIONS DE NAVIER STOKES DETERMINISTES ET STOCHASTIQUES ET SUR UNE EQUATION ELLIPTIQUE written by MARIANA.. MILITARU and published by . This book was released on 1997 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: CETTE THESE, EST CONSTITUEE PAR TROIS PROBLEMES SUR DES CONDITIONS AUX LIMITES MIXTES LIES AUX EQUATIONS ELLIPTIQUES ET DE NAVIER-STOKES. DANS LA PREMIERE PARTIE, ON MONTRE L'EXISTENCE D'UNE SOLUTION FAIBLE D'UNE EQUATION DE NAVIER-STOKES STOCHASTIQUE, LORSQUE LA DENSITE INITIALE S'ANNULE. APRES AVOIR OBTENU DES ESTIMATIONS CONVENABLES SUR DES SOLUTIONS APPROCHEES, ON EN DEDUIT LA CONVERGENCE EN LOI DANS UN NOUVEL ESPACE DE PROBABILITE. PAR UN PASSAGE A LA LIMITE ELLE OBTIENT ALORS UNE SOLUTION VERIFIANT UNE EQUATION SOUS FORME D'UNE ESPERANCE, DONC UNE SOLUTION FAIBLE. DANS LA SECONDE PARTIE, ON MONTRE L'EXISTENCE D'UNE SOLUTION DE L'EQUATION DE NAVIER STOKES A DENSITE VARIABLE EN DIMENSION 2. ON A ETUDIE LE CAS OU LA VITESSE EST NULLE SUR UNE PARTIE ET OU SUR UNE AUTRE PARTIE LA VITESSE TANGENTIELLE EST NULLE ET LA PRESSION DYNAMIQUE EST FIXEE. ON MONTRE L'EXISTENCE DANS UN ESPACE DE DIMENSION FINIE ET ENSUITE PAR PASSAGE A LA LIMITE, ON A OBTENU L'EXISTENCE D'UNE SOLUTION DANS UN ESPACE DE SOBOLEV. DANS LA TROISIEME PARTIE, ON ETABLIT L'EXISTENCE ET LA REGULARITE D'UNE SOLUTION D'UN PROBLEME ELLIPTIQUE DANS UN CYLINDRE, AVEC DES CONDITIONS AUX LIMITES MIXTES : DE TYPE NEUMANN OU LA SOLUTION NE DEPEND QUE DE LA HAUTEUR SUR LA FRONTIERE LATERALE. ON A UTILISE UNE METHODE QUI CARACTERISE DES ESPACES DE SOBOLEV, BASEE SUR DES ESTIMATIONS SUIVANT DES CHAMPS TANGENTIELLES A LA FRONTIERE.

Download or read book Finite Element Methods and Navier Stokes Equations written by C. Cuvelier and published by Springer Science & Business Media. This book was released on 1986-03-31 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: