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Fundamental Directions in Mathematical Fluid Mechanics - edition reliée, livre de poche

2000, ISBN: 3764364149

[EAN: 9783764364144], Nouveau livre, [SC: 10.99], [PU: Birkhäuser Basel], BOUNDARYVALUEPROBLEM; FLUIDDYNAMICS; NAVIER-STOKESEQUATION; NAVIER-STOKESEQUATIONS; FINITEELEMENTMETHOD; FLUIDGEO… Plus…

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ISBN: 9783764364144

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, putt… Plus…

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ISBN: 9783764364144

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, putt… Plus…

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Fundamental Directions in Mathematical Fluid Mechanics - edition reliée, livre de poche

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Fundamental Directions in Mathematical Fluid Mechanics - Giovanni P. Galdi; John G. Heywood; Rolf Rannacher
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Giovanni P. Galdi; John G. Heywood; Rolf Rannacher:
Fundamental Directions in Mathematical Fluid Mechanics - Première édition

2000, ISBN: 9783764364144

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Fundamental Directions in Mathematical Fluid Mechanics
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ISBN:

3764364149


This set of six papers, written by eminent experts in the field, is concerned with that part of fluid mechanics that seeks its foundation in the rigorous mathematical treatment of the Navier-Stokes equations. In particular, an overview is given on state of research regarding the global existence of smooth solutions, for which uniqueness and continuous dependence on the data can be proven. Then, the book moves on to a discussion of recent developments of the finite element Galerkin method, with an emphasis on a priori and a posteriori error estimation and adaptive mesh refinement. A further article elaborates on spectral Galerkin methods and their extension to domains with complicated geometries by employing the techniques of domain decomposition. The rigorous explanation of bifurcation phenomena in fluids has long been a central topic in the theory of Navier-Stokes equations. Here, bifurcation theory is introduced in a general setting that is particularly convenient for application to such problems. Finally, the extension of Navier-Stokes theory to compressible viscous flows, studied in two more papers, opens up a fascinating panorama of theoretical and numerical problems. While some of the contributions are expository, others primarily present new results within a wider context and fuller exposition than is usual for research papers. The book is meant to introduce researchers and advanced students to the research level on some of the most important topics of the field.

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EAN (ISBN-13): 9783764364144
ISBN (ISBN-10): 3764364149
Version reliée
Date de parution: 2000
Editeur: Springer Basel
304 Pages
Poids: 0,699 kg
Langue: eng/Englisch

Livre dans la base de données depuis 2007-11-01T16:05:00+01:00 (Zurich)
Page de détail modifiée en dernier sur 2024-03-13T14:05:58+01:00 (Zurich)
ISBN/EAN: 3764364149

ISBN - Autres types d'écriture:
3-7643-6414-9, 978-3-7643-6414-4
Autres types d'écriture et termes associés:
Auteur du livre: rannacher, galdi, john giovanni
Titre du livre: mathematical, fluid mechanics, fundamental

Données de l'éditeur

Auteur: Giovanni P. Galdi; John G. Heywood; Rolf Rannacher
Titre: Advances in Mathematical Fluid Mechanics; Fundamental Directions in Mathematical Fluid Mechanics
Editeur: Birkhäuser; Springer Basel
293 Pages
Date de parution: 2000-09-01
Basel; CH
Langue: Anglais
106,99 € (DE)
109,99 € (AT)
118,00 CHF (CH)
Available
VIII, 293 p.

BB; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Boundary value problem; Fluid dynamics; Navier-Stokes equation; Navier-Stokes equations; finite element method; fluid mechanics; geometry; mechanics; Analysis; Mathematical Physics; Classical Mechanics; Mathematische Physik; Klassische Mechanik; BC

An Introduction to the Navier-Stokes Initial-Boundary Value Problem.- 0 Introduction.- 1 Some considerations on the structure of the Navier-Stokes equations.- 2 The Leray-Hopf weak solutions and related properties.- 3 Existence of weak solutions.- 4 The energy equality and uniqueness of weak solutions.- 5 Regularity of weak solutions.- 6 More regular solutions and the “théorème de structure”.- 7 Existence in the class Lr (0,T; Ls(?), 2/r +n/s = 1, and further regularity properties.- References.- Spectral Approximation of Navier-Stokes Equations.- 1 Mathematical foundation and different paradigms of spectral methods.- 2 Stokes and Navier-Stokes equations.- 3 Time-differentiation of Navier Stokes equations.- 4 Domain decomposition methods.- 5 Numerical results.- References.- Simple Proofs of Bifurcation Theorems.- 1 Introduction.- 2 Bifurcation of equilibrium solutions.- 3 Bifurcation of periodic solutions.- 4 Generalizations.- Appendix A: Proof of Proposition 3.1.- References.- On The Steady Transport Equation.- 1 Introduction.- 2 Existence in W1,2 ? Lq for the scalar transport equation.- 3 Existence in W1,2 ? Lq for the scalar transport equation.- 4 Estimates for ???2,2, ???? and ?????1,2.- 5 Existence in Wm,2 (?), for any fixed m.- 6 Integration along characteristics.- References.- On the Existence and Uniqueness Theory for the Steady Compressible Viscous Flow.- 1 Introduction.- 2 Poisson-Stokes equations for isothermal flow.- 3 Main result.- 4 Iterative scheme.- 5 Regularity lemmas.- 6 Bounds for the iterates.- 7 Convergence of the iterates.- 8 Uniqueness in the ball of existence.- 9 Uniqueness reconsidered directly.- References.- Finite Element Methods for the Incompressible Navier-Stokes Equations.- 1 Introduction.- 2 Models of viscousflow.- 3 Spatial discretization by finite elements.- 4 Time discretization and linearization.- 5 Solution of the algebraic systems.- 6 A review of theoretical analysis.- 7 Error control and mesh adaptation.- 8 Extension to weakly compressible flows.- References.
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