Mathematical theory of incompressible nonviscous fluids:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Springer
1994
|
| Schriftenreihe: | Applied mathematical sciences
96 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005537759&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 283 S. graph. Darst. |
| ISBN: | 0387940448 3540940448 |
Internformat
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| 100 | 1 | |a Marchioro, Carlo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical theory of incompressible nonviscous fluids |c Carlo Marchioro ; Mario Pulvirenti |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1994 | |
| 300 | |a XI, 283 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202 PHY 221f 2002 A 3529 |
|---|---|
| DE-BY-TUM_katkey | 609109 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040020613578 |
| _version_ | 1821931066205667328 |
| adam_text | Contents
Preface v
Chapter 1
General Considerations on the Euler Equation 1
1.1. The Equation of Motion of an Ideal Incompressible Fluid 1
1.2. Vorticity and Stream Function 9
1.3. Conservation Laws 23
1.4. Potential and Irrotational Flows 33
1.5. Comments 40
Appendix 1.1 (Liouville Theorem) 48
Appendix 1.2 (A Decomposition Theorem) 49
Appendix 1.3 (Kutta Joukowski Theorem and Complex Potentials) . 50
Appendix 1.4 (d Alembert Paradox) 52
Exercises 55
Chapter 2
Construction of the Solutions 59
2.1. General Considerations 59
2.2. Lagrangian Representation of the Vorticity 63
2.3. Global Existence and Uniqueness in Two Dimensions 66
2.4. Regularity Properties and Classical Solutions 72
2.5. Local Existence and Uniqueness in Three Dimensions 74
2.6. Some Heuristic Considerations on the Three Dimensional
Motion 78
2.7. Comments 80
Appendix 2.1 (Integral Inequalities) 86
ix
x Contents
Appendix 2.2 (Some Useful Inequalities) 87
Appendix 2.3 (Quasi Lipschitz Estimate) 89
Appendix 2.4 (Regularity Estimates) 89
Exercises 90
Chapter 3
Stability of Stationary Solutions of the Euler Equation 93
3.1. A Short Review of the Stability Concept 93
3.2. Sufficient Conditions for the Stability of Stationary Solutions:
The Arnold Theorems 104
3.3. Stability in the Presence of Symmetries 115
3.4. Instability 120
3.5. Comments 128
Exercises 132
Chapter 4
The Vortex Model 134
4.1. Heuristic Introduction 134
4.2. Motion of Vortices in the Plane 137
4.3. The Vortex Motion in the Presence of Boundaries 152
4.4. A Rigorous Derivation of the Vortex Model 157
4.5. Three Dimensional Models 166
4.6. Comments 169
Exercises 176
Chapter 5
Approximation Methods 178
5.1. Introduction 178
5.2. Spectral Methods 179
5.3. Vortex Methods 182
5.4. Comments 186
Appendix 5.1 (On K R Distance) 188
Exercises 189
Chapter 6
Evolution of Discontinuities 191
6.1. Vortex Sheet 191
6.2. Existence and Behavior of the Solutions 200
6.3. Comments 207
6.4. Spatially Inhomogeneous Fluids 211
6.5. Water Waves 212
6.6. Approximations 219
Appendix 6.1 (Proof of a Theorem of the Cauchy Kowalevski Type) 227
Appendix 6.2 (On Surface Tension) 228
Contents xi
Chapter 7
Turbulence 230
7.1. Introduction 230
7.2. The Onset of Turbulence 234
7.3. Phenomenological Theories 246
7.4. Statistical Solutions and Invariant Measures 250
7.5. Statistical Mechanics of Vortex Systems 256
7.6. Three Dimensional Models for Turbulence 268
References 272
Index 281
|
| any_adam_object | 1 |
| author | Marchioro, Carlo Pulvirenti, Mario |
| author_facet | Marchioro, Carlo Pulvirenti, Mario |
| author_role | aut aut |
| author_sort | Marchioro, Carlo |
| author_variant | c m cm m p mp |
| building | Verbundindex |
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| classification_tum | PHY 221f |
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| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV008407826 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:21:12Z |
| institution | BVB |
| isbn | 0387940448 3540940448 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005537759 |
| oclc_num | 231579689 |
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| owner | DE-703 DE-384 DE-20 DE-12 DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-703 DE-384 DE-20 DE-12 DE-29T DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XI, 283 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spellingShingle | Marchioro, Carlo Pulvirenti, Mario Mathematical theory of incompressible nonviscous fluids Applied mathematical sciences Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd Hydrodynamik (DE-588)4026302-2 gnd Lagrange-Bewegungsgleichungen (DE-588)4166460-7 gnd Ideale Flüssigkeit (DE-588)4161200-0 gnd Inkompressible Strömung (DE-588)4129759-3 gnd Strömungsmechanik (DE-588)4077970-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4219070-8 (DE-588)4026302-2 (DE-588)4166460-7 (DE-588)4161200-0 (DE-588)4129759-3 (DE-588)4077970-1 (DE-588)4114528-8 |
| title | Mathematical theory of incompressible nonviscous fluids |
| title_auth | Mathematical theory of incompressible nonviscous fluids |
| title_exact_search | Mathematical theory of incompressible nonviscous fluids |
| title_full | Mathematical theory of incompressible nonviscous fluids Carlo Marchioro ; Mario Pulvirenti |
| title_fullStr | Mathematical theory of incompressible nonviscous fluids Carlo Marchioro ; Mario Pulvirenti |
| title_full_unstemmed | Mathematical theory of incompressible nonviscous fluids Carlo Marchioro ; Mario Pulvirenti |
| title_short | Mathematical theory of incompressible nonviscous fluids |
| title_sort | mathematical theory of incompressible nonviscous fluids |
| topic | Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd Hydrodynamik (DE-588)4026302-2 gnd Lagrange-Bewegungsgleichungen (DE-588)4166460-7 gnd Ideale Flüssigkeit (DE-588)4161200-0 gnd Inkompressible Strömung (DE-588)4129759-3 gnd Strömungsmechanik (DE-588)4077970-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Eulersche Bewegungsgleichungen Hydrodynamik Lagrange-Bewegungsgleichungen Ideale Flüssigkeit Inkompressible Strömung Strömungsmechanik Mathematisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005537759&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT marchiorocarlo mathematicaltheoryofincompressiblenonviscousfluids AT pulvirentimario mathematicaltheoryofincompressiblenonviscousfluids |
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Teilbibliothek Physik
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0202 PHY 221f 2002 A 3529
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