Applied analysis of the Navier Stokes equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge <<[u.a.]>>
Cambridge Univ. Press
1995
|
| Ausgabe: | 1 |
| Schriftenreihe: | Cambridge Texts in applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 217 S. graph. Darst. |
| ISBN: | 052144568X |
Internformat
MARC
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| 100 | 1 | |a Doering, Charles R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applied analysis of the Navier Stokes equations |c Charles R. Doering ; J. D. Gibbon |
| 250 | |a 1 | ||
| 264 | 1 | |a Cambridge <<[u.a.]>> |b Cambridge Univ. Press |c 1995 | |
| 300 | |a XIII, 217 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804140485255626752 |
|---|---|
| adam_text | Contents
Preface page xi
1 The equations of motion 1
1.1 Introduction 1
1.2 Euler s equations for an incompressible fluid 1
1.3 Energy, body forces, vorticity, and enstrophy 7
1.4 Viscosity, the stress tensor, and the Navier-Stokes equations 12
1.5 Thermal convection and the Boussinesq equations 18
1.6 References and further reading 21
Exercises 22
2 Dimensionless parameters and stability 23
2.1 Dimensionless parameters 23
2.2 Linear and nonlinear stability, differential inequalities 29
2.3 References and further reading 38
Exercises 38
3 Turbulence 40
3.1 Introduction 40
3.2 Statistical turbulence theory and the closure problem 40
3.3 Spectra, Kolmogorov s scaling theory, and turbulent length
scales 49
3.4 References and further reading 59
Exercises 60
4 Degrees of freedom, dynamical systems, and attractors 61
4.1 Introduction 61
4.2 Dynamical systems, attractors, and their dimension 62
vii
viii Contents
4.3 The Lorenz system 74
4.4 References and further reading 86
Exercises 87
5 On the existence, uniqueness, and regularity of solutions 88
5.1 Introduction 88
5.2 Existence and uniqueness for ODEs 89
5.3 Galerkin approximations and weak solutions of the Navier-
Stokes equations 96
5.4 Uniqueness and the regularity problem 104
5.5 References and further reading 113
Exercises 113
6 Ladder results for the Navier-Stokes equations 114
6.1 Introduction 114
6.2 The Navier-Stokes ladder theorem 117
6.3 A natural definition of a length scale 125
6.4 The dynamical wavenumbers Ks,r 127
6.5 Estimates for the Navier-Stokes equations 128
6.5.1 Estimates for Fo 129
6.5.2 Estimates for {Fi) and (k210) 130
6.5.3 Estimates for BmV-^Fi, (F2), and k|j 131
6.6 A ladder for the thermal convection equations 132
6.7 References and further reading 134
Exercises 134
7 Regularity and length scales for the Id and 3d Navier-Stokes
equations 137
7.1 Introduction 137
7.2 Regularity and length scales in the Id case 138
7.3 The 3d regularity problem and the ||u||3+8 result 142
7.4 An infinite set of time averaged quantities 143
7.5 The Kolmogorov length and intermittency 145
7.6 Breakdown of regularity 149
7.6.1 Theroleof/JllDulUr)^ 149
7.6.2 Breakdown of regularity beyond small initial data 150
7.7 Weak singularities and length scales 151
7.8 Singularities and the Euler equations 153
7.9 References and further reading 156
Exercises 157
Contents ix
8 Exponential decay of the Fourier power spectrum 158
8.1 Introduction 158
8.2 A differential inequality for He^Vu^ 158
8.3 A bound on ||eat|V|Vu||2 164
8.4 Decay of the Fourier spectrum 166
8.5 References and further reading 168
Exercises 168
9 The attractor dimension for the Navier-Stokes equations 170
9.1 Introduction 170
9.2 The Id attractor dimension estimate 171
9.3 The 3d attractor dimension estimate 178
9.4 References and further reading 180
Exercises 181
10 Energy dissipation rate estimates for boundary-driven flows 182
10.1 Introduction 182
10.2 Boundary-driven shear flow 183
10.3 Thermal convection in a horizontal plane 193
10.4 Discussion 198
10.5 References and further reading 204
Exercises 205
Appendix A Inequalities 206
References 210
Index 213
|
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| institution | BVB |
| isbn | 052144568X |
| language | English |
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| physical | XIII, 217 S. graph. Darst. |
| publishDate | 1995 |
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| series2 | Cambridge Texts in applied mathematics |
| spelling | Doering, Charles R. Verfasser aut Applied analysis of the Navier Stokes equations Charles R. Doering ; J. D. Gibbon 1 Cambridge <<[u.a.]>> Cambridge Univ. Press 1995 XIII, 217 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge Texts in applied mathematics Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 s 1\p DE-604 Gibbon, J. D. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018466845&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Doering, Charles R. Gibbon, J. D. Applied analysis of the Navier Stokes equations Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| subject_GND | (DE-588)4041456-5 |
| title | Applied analysis of the Navier Stokes equations |
| title_auth | Applied analysis of the Navier Stokes equations |
| title_exact_search | Applied analysis of the Navier Stokes equations |
| title_full | Applied analysis of the Navier Stokes equations Charles R. Doering ; J. D. Gibbon |
| title_fullStr | Applied analysis of the Navier Stokes equations Charles R. Doering ; J. D. Gibbon |
| title_full_unstemmed | Applied analysis of the Navier Stokes equations Charles R. Doering ; J. D. Gibbon |
| title_short | Applied analysis of the Navier Stokes equations |
| title_sort | applied analysis of the navier stokes equations |
| topic | Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| topic_facet | Navier-Stokes-Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018466845&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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