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Bibliographic Details
Main Author:	Foiaş, Ciprian 1933-2020 (Author)
Format:	Book
Language:	English
Published:	Cambridge Cambridge University Press 2001
Edition:	1. published
Series:	Encyclopedia of mathematics and its applications 83
Subjects:	Equações de navier-stokes Navier-Stokes, Équations de Navier-Stokes-vergelijkingen Turbulence Turbulentie Turbulência Navier-Stokes equations Navier-Stokes-Gleichung Turbulente Strömung
Links:	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
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XIV, 347 Seiten
ISBN:	0521360323 9780521360326

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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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series	Encyclopedia of mathematics and its applications
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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
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volume_link	(DE-604)BV000903719
work_keys_str_mv	AT foiasciprian navierstokesequationsandturbulence

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