Navier-Stokes equations and turbulence:
This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by t...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2001
|
| Series: | Encyclopedia of mathematics and its applications
volume 83 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyse turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier–Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers and physicists |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xiv, 347 pages) |
| ISBN: | 9780511546754 |
| DOI: | 10.1017/CBO9780511546754 |
Staff View
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| 505 | 8 | 0 | |t Introduction and Overview of Turbulence |t Viscous Fluids. The Navier-Stokes Equations |t Turbulence: Where the Interests of Engineers and Mathematicians Overlap |t Elements of the Theories of Turbulence of Kolmogorov and Kraichnan |t Function Spaces, Functional Inequalities, and Dimensional Analysis |t Elements of the Mathematical Theory of the Navier-Stokes Equations |t Energy and Enstrophy |t Boundary Value Problems |t Helmholtz-Leray Decomposition of Vector Fields |t Weak Formulation of the Navier-Stokes Equations |t Function Spaces |t The Stokes Operator |t Existence and Uniqueness of Solutions: The Main Results |t Analyticity in Time |t Gevrey Class Regularity and the Decay of the Fourier Coefficients |t Function Spaces for the Whole-Space Case |t The No-Slip Case with Moving Boundaries |t Dissipation Rate of Flows |t Nondimensional Estimates and the Grashof Number |t Mathematical Complements |t Proofs of Technical Results in Chapter II |t Finite Dimensionality of Flows |t Determining Modes |t Determining Nodes |t Attractors and Their Fractal Dimension |t Approximate Inertial Manifolds |t Proofs of Technical Results in Chapter III |t Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors |t Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits |t Invariant Measures and Stationary Statistical Solutions in Dimension 2 |t Stationary Statistical Solutions in Dimension 3 |t Attractors and Stationary Statistical Solutions |
| 520 | |a This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyse turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier–Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers and physicists | ||
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Record in the Search Index
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| any_adam_object | |
| author | Foiaş, Ciprian |
| author_facet | Foiaş, Ciprian |
| author_role | aut |
| author_sort | Foiaş, Ciprian |
| author_variant | c f cf |
| building | Verbundindex |
| bvnumber | BV043941273 |
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| contents | Introduction and Overview of Turbulence Viscous Fluids. The Navier-Stokes Equations Turbulence: Where the Interests of Engineers and Mathematicians Overlap Elements of the Theories of Turbulence of Kolmogorov and Kraichnan Function Spaces, Functional Inequalities, and Dimensional Analysis Elements of the Mathematical Theory of the Navier-Stokes Equations Energy and Enstrophy Boundary Value Problems Helmholtz-Leray Decomposition of Vector Fields Weak Formulation of the Navier-Stokes Equations Function Spaces The Stokes Operator Existence and Uniqueness of Solutions: The Main Results Analyticity in Time Gevrey Class Regularity and the Decay of the Fourier Coefficients Function Spaces for the Whole-Space Case The No-Slip Case with Moving Boundaries Dissipation Rate of Flows Nondimensional Estimates and the Grashof Number Mathematical Complements Proofs of Technical Results in Chapter II Finite Dimensionality of Flows Determining Modes Determining Nodes Attractors and Their Fractal Dimension Approximate Inertial Manifolds Proofs of Technical Results in Chapter III Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits Invariant Measures and Stationary Statistical Solutions in Dimension 2 Stationary Statistical Solutions in Dimension 3 Attractors and Stationary Statistical Solutions |
| ctrlnum | (ZDB-20-CBO)CR9780511546754 (OCoLC)849876933 (DE-599)BVBBV043941273 |
| dewey-full | 532/.0527 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.0527 |
| dewey-search | 532/.0527 |
| dewey-sort | 3532 3527 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/CBO9780511546754 |
| format | Electronic eBook |
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| id | DE-604.BV043941273 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:15Z |
| institution | BVB |
| isbn | 9780511546754 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350244 |
| oclc_num | 849876933 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xiv, 347 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2001 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Foiaş, Ciprian Verfasser aut Navier-Stokes equations and turbulence C. Foias [and three others] Navier-Stokes Equations & Turbulence Cambridge Cambridge University Press 2001 1 online resource (xiv, 347 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 83 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Introduction and Overview of Turbulence Viscous Fluids. The Navier-Stokes Equations Turbulence: Where the Interests of Engineers and Mathematicians Overlap Elements of the Theories of Turbulence of Kolmogorov and Kraichnan Function Spaces, Functional Inequalities, and Dimensional Analysis Elements of the Mathematical Theory of the Navier-Stokes Equations Energy and Enstrophy Boundary Value Problems Helmholtz-Leray Decomposition of Vector Fields Weak Formulation of the Navier-Stokes Equations Function Spaces The Stokes Operator Existence and Uniqueness of Solutions: The Main Results Analyticity in Time Gevrey Class Regularity and the Decay of the Fourier Coefficients Function Spaces for the Whole-Space Case The No-Slip Case with Moving Boundaries Dissipation Rate of Flows Nondimensional Estimates and the Grashof Number Mathematical Complements Proofs of Technical Results in Chapter II Finite Dimensionality of Flows Determining Modes Determining Nodes Attractors and Their Fractal Dimension Approximate Inertial Manifolds Proofs of Technical Results in Chapter III Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits Invariant Measures and Stationary Statistical Solutions in Dimension 2 Stationary Statistical Solutions in Dimension 3 Attractors and Stationary Statistical Solutions This book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyse turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier–Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers and physicists Turbulence Navier-Stokes equations Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Turbulente Strömung (DE-588)4117265-6 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 s Turbulente Strömung (DE-588)4117265-6 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-06460-6 Erscheint auch als Druckausgabe 978-0-521-36032-6 https://doi.org/10.1017/CBO9780511546754 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Foiaş, Ciprian Navier-Stokes equations and turbulence Introduction and Overview of Turbulence Viscous Fluids. The Navier-Stokes Equations Turbulence: Where the Interests of Engineers and Mathematicians Overlap Elements of the Theories of Turbulence of Kolmogorov and Kraichnan Function Spaces, Functional Inequalities, and Dimensional Analysis Elements of the Mathematical Theory of the Navier-Stokes Equations Energy and Enstrophy Boundary Value Problems Helmholtz-Leray Decomposition of Vector Fields Weak Formulation of the Navier-Stokes Equations Function Spaces The Stokes Operator Existence and Uniqueness of Solutions: The Main Results Analyticity in Time Gevrey Class Regularity and the Decay of the Fourier Coefficients Function Spaces for the Whole-Space Case The No-Slip Case with Moving Boundaries Dissipation Rate of Flows Nondimensional Estimates and the Grashof Number Mathematical Complements Proofs of Technical Results in Chapter II Finite Dimensionality of Flows Determining Modes Determining Nodes Attractors and Their Fractal Dimension Approximate Inertial Manifolds Proofs of Technical Results in Chapter III Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits Invariant Measures and Stationary Statistical Solutions in Dimension 2 Stationary Statistical Solutions in Dimension 3 Attractors and Stationary Statistical Solutions Turbulence Navier-Stokes equations Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| subject_GND | (DE-588)4041456-5 (DE-588)4117265-6 |
| title | Navier-Stokes equations and turbulence |
| title_alt | Navier-Stokes Equations & Turbulence Introduction and Overview of Turbulence Viscous Fluids. The Navier-Stokes Equations Turbulence: Where the Interests of Engineers and Mathematicians Overlap Elements of the Theories of Turbulence of Kolmogorov and Kraichnan Function Spaces, Functional Inequalities, and Dimensional Analysis Elements of the Mathematical Theory of the Navier-Stokes Equations Energy and Enstrophy Boundary Value Problems Helmholtz-Leray Decomposition of Vector Fields Weak Formulation of the Navier-Stokes Equations Function Spaces The Stokes Operator Existence and Uniqueness of Solutions: The Main Results Analyticity in Time Gevrey Class Regularity and the Decay of the Fourier Coefficients Function Spaces for the Whole-Space Case The No-Slip Case with Moving Boundaries Dissipation Rate of Flows Nondimensional Estimates and the Grashof Number Mathematical Complements Proofs of Technical Results in Chapter II Finite Dimensionality of Flows Determining Modes Determining Nodes Attractors and Their Fractal Dimension Approximate Inertial Manifolds Proofs of Technical Results in Chapter III Stationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors Mathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits Invariant Measures and Stationary Statistical Solutions in Dimension 2 Stationary Statistical Solutions in Dimension 3 Attractors and Stationary Statistical Solutions |
| title_auth | Navier-Stokes equations and turbulence |
| title_exact_search | Navier-Stokes equations and turbulence |
| title_full | Navier-Stokes equations and turbulence C. Foias [and three others] |
| title_fullStr | Navier-Stokes equations and turbulence C. Foias [and three others] |
| title_full_unstemmed | Navier-Stokes equations and turbulence C. Foias [and three others] |
| title_short | Navier-Stokes equations and turbulence |
| title_sort | navier stokes equations and turbulence |
| topic | Turbulence Navier-Stokes equations Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| topic_facet | Turbulence Navier-Stokes equations Navier-Stokes-Gleichung Turbulente Strömung |
| url | https://doi.org/10.1017/CBO9780511546754 |
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