Navier-Stokes equations and turbulence
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2001
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| Ausgabe: | 1. published |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
83 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Navier-Stokes equations and turbulence |c C. Foias ; O. Manley ; R. Rosa ; R. Temam |
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| 650 | 4 | |a Turbulence | |
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Datensatz im Suchindex
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| adam_text | ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS NAVIER-STOKES EQUATIONS
AND TURBULENCE C. FOIAS O. MANLEY R. ROSA R. TEMAM CAMBRIDGE UNIVERSITY
PRESS CONTENTS PREFACE PAGE IX ACKNOWLEDGMENTS XIV CHAPTER I
INTRODUCTION AND OVERVIEW OF TURBULENCE 1 INTRODUCTION 1 1. VISCOUS
FLUIDS. THE NAVIER-STOKES EQUATIONS 1 2. TURBULENCE: WHERE THE INTERESTS
OF ENGINEERS AND MATHEMATICIANS OVERLAP 5 3. ELEMENTS OF THE THEORIES OF
TURBULENCE OF KOLMOGOROV AND KRAICHNAN 9 4. FUNCTION SPACES, FUNCTIONAL
INEQUALITIES, AND DIMENSIONAL ANALYSIS 14 CHAPTER II ELEMENTS OF THE
MATHEMATICAL THEORY OF THE NAVIER-STOKES EQUATIONS 25 INTRODUCTION 25 1.
ENERGY AND ENSTROPHY 27 2. BOUNDARY VALUE PROBLEMS 29 3. HELMHOLTZ-LERAY
DECOMPOSITION OF VECTOR FIELDS 36 4. WEAK FORMULATION OF THE
NAVIER-STOKES EQUATIONS 39 5. FUNCTION SPACES 41 6. THE STOKES OPERATOR
49 7. EXISTENCE AND UNIQUENESS OF SOLUTIONS: THE MAIN RESULTS 55 8.
ANALYTICITY IN TIME 62 9. GEVREY CLASS REGULARITY AND THE DECAY OF THE
FOURIER COEFFICIENTS 67 10. FUNCTION SPACES FOR THE WHOLE-SPACE CASE 75
11. THE NO-SLIP CASE WITH MOVING BOUNDARIES 77 12. DISSIPATION RATE OF
HOWS 80 13. NONDIMENSIONAL ESTIMATES AND THE GRASHOF NUMBER 87 APPENDIX
A. MATHEMATICAL COMPLEMENTS 90 APPENDIX B. PROOFS OF TECHNICAL RESULTS
IN CHAPTER II 102 VIII CONTENTS CHAPTER III FINITE DIMENSIONALITY OF
FLOWS 115 INTRODUCTION 115 1. DETERMINING MODES 123 2. DETERMINING NODES
131 3. ATTRACTORS AND THEIR FRACTAL DIMENSION 137 4. APPROXIMATE
INERTIAL MANIFOLDS 150 APPENDIX A. PROOFS OF TECHNICAL RESULTS IN
CHAPTER III 156 CHAPTER IV STATIONARY STATISTICAL SOLUTIONS OF THE
NAVIER-STOKES EQUATIONS, TIME AVERAGES, AND ATTRACTORS 1 69 INTRODUCTION
169 1. MATHEMATICAL FRAMEWORK, DEFINITION OF STATIONARY STATISTICAL
SOLUTIONS, AND BANACH GENERALIZED LIMITS 172 2. INVARIANT MEASURES AND
STATIONARY STATISTICAL SOLUTIONS IN DIMENSION 2 183 3. STATIONARY
STATISTICAL SOLUTIONS IN DIMENSION 3 189 4. ATTRACTORS AND STATIONARY
STATISTICAL SOLUTIONS 194 5. AVERAGE TRANSFER OF ENERGY AND THE CASCADES
IN TURBULENT FLOWS 198 APPENDIX A. NEW CONCEPTS AND RESULTS USED IN
CHAPTER IV 218 APPENDIX B. PROOFS OF TECHNICAL RESULTS IN CHAPTER IV 227
APPENDIX C. A MATHEMATICAL COMPLEMENT: THE ACCRETIVITY PROPERTY IN
DIMENSION 3 244 CHAPTER V TIME -DEPENDENT STATISTICAL SOLUTIONS OF THE
NAVIER-STOKES EQUATIONS AND FULLY DEVELOPED TURBULENCE 255 INTRODUCTION
255 1. TIME-DEPENDENT STATISTICAL SOLUTIONS ON BOUNDED DOMAINS 262 2.
HOMOGENEOUS STATISTICAL SOLUTIONS 271 3. REYNOLDS EQUATION FOR THE
AVERAGE FLOW 280 4. SELF-SIMILAR HOMOGENEOUS STATISTICAL SOLUTIONS 283
5. RELATION WITH AND APPLICATION TO THE CONVENTIONAL THEORY OF
TURBULENCE 295 6. SOME CONCLUDING REMARKS 310 APPENDIX A. PROOFS OF
TECHNICAL RESULTS IN CHAPTER V 312 REFERENCES 331 INDEX 343
|
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| author | Foiaş, Ciprian 1933-2020 |
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| discipline | Physik Mathematik |
| edition | 1. published |
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| indexdate | 2024-12-23T15:47:19Z |
| institution | BVB |
| isbn | 0521360323 9780521360326 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009652354 |
| oclc_num | 45314067 |
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| physical | XIV, 347 Seiten |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spellingShingle | Foiaş, Ciprian 1933-2020 Navier-Stokes equations and turbulence Encyclopedia of mathematics and its applications Equações de navier-stokes larpcal Navier-Stokes, Équations de Navier-Stokes-vergelijkingen gtt Turbulence Turbulentie gtt Turbulência larpcal 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_auth | Navier-Stokes equations and turbulence |
| title_exact_search | Navier-Stokes equations and turbulence |
| title_full | Navier-Stokes equations and turbulence C. Foias ; O. Manley ; R. Rosa ; R. Temam |
| title_fullStr | Navier-Stokes equations and turbulence C. Foias ; O. Manley ; R. Rosa ; R. Temam |
| title_full_unstemmed | Navier-Stokes equations and turbulence C. Foias ; O. Manley ; R. Rosa ; R. Temam |
| title_short | Navier-Stokes equations and turbulence |
| title_sort | navier stokes equations and turbulence |
| topic | Equações de navier-stokes larpcal Navier-Stokes, Équations de Navier-Stokes-vergelijkingen gtt Turbulence Turbulentie gtt Turbulência larpcal Navier-Stokes equations Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Turbulente Strömung (DE-588)4117265-6 gnd |
| topic_facet | Equações de navier-stokes Navier-Stokes, Équations de Navier-Stokes-vergelijkingen Turbulence Turbulentie Turbulência Navier-Stokes equations Navier-Stokes-Gleichung Turbulente Strömung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009652354&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT foiasciprian navierstokesequationsandturbulence |