Nonstandard methods for stochastic fluid mechanics
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| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore u.a.
World Scientific
1995
|
| Schriftenreihe: | Series on advances in mathematics for applied sciences
27 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Capiński, Marek |d 1951- |e Verfasser |0 (DE-588)172897866 |4 aut | |
| 245 | 1 | 0 | |a Nonstandard methods for stochastic fluid mechanics |c Marek Capiński ; Nigel J. Cutland |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1995 | |
| 300 | |a XII, 227 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Series on advances in mathematics for applied sciences |v 27 | |
| 650 | 7 | |a Analyse mathématique non standard |2 ram | |
| 650 | 7 | |a Fluides, mécanique des |2 ram | |
| 650 | 7 | |a Processus stochastiques |2 ram | |
| 650 | 4 | |a Fluid mechanics | |
| 650 | 4 | |a Nonstandard mathematical analysis | |
| 650 | 4 | |a Stochastic processes | |
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| 689 | 0 | 2 | |a Nonstandard-Analysis |0 (DE-588)4137021-1 |D s |
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| 700 | 1 | |a Cutland, Nigel J. |e Verfasser |4 aut | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006995233 | |
Datensatz im Suchindex
| _version_ | 1819769323869175808 |
|---|---|
| adam_text | Contents
Preface vii
1 Standard Preliminaries 1
1.1 Functional Analysis 1
1.2 Stochastic Analysis 5
2 Nonstandard Preliminaries 11
2.1 Construction of *IR 12
2.2 The Transfer Principle for *]R 18
2.3 Internal Sets and Functions 21
2.4 The Hilbert Space H 30
2.5 Countable Comprehension and Ni Saturation 31
2.6 Topology 34
2.7 Hilbert Spaces 39
3 Loeb Measure and Integration Theory 47
3.1 The Loeb Construction 47
3.2 Representations of Standard Measures 50
3.3 Loeb Measurable Functions and Integration 54
3.4 Nonstandard Densities of Measures on Hilbert Spaces 60
3.5 Bochner Integration 64
3.6 Stochastic Integration in Hilbert Spaces 68
4 Weak Solutions of Navier Stokes Equations 77
4.1 Definition of Solutions and Galerkin Approximations 78
4.2 Existence of Solutions 79
4.3 The Uniqueness Problem 86
4.4 Notes 92
5 Statistical Solutions of Navier Stokes Equations 93
5.1 Space time Solutions 95
5.2 Spatial Solutions 100
5.3 Statistical Solutions Using Nonstandard Densities 103
xi
xii Contents
5.4 The Hopf Equation 111
5.5 Uniqueness of Statistical Solutions 116
5.6 Intrinsic Turbulence 122
5.7 Notes 129
6 Stochastic Navier Stokes Equations 131
6.1 Definition of Solution 132
6.2 Solution of a Particular Case 133
6.3 A Special Case of Multiplicative Noise 138
6.4 The General Case: Existence 145
6.5 Regularity of Solutions 152
6.6 Uniqueness Theorems 159
6.7 Thermohydraulics 164
6.8 Notes 167
7 Statistical Solutions of Stochastic Navier Stokes Equations 169
7.1 The Foias Equation 169
7.2 The Hopf Equation 173
7.3 Statistical Solutions by Nonstandard Densities 175
7.4 Notes 183
8 The Euler Equation 185
8.1 The General Case 185
8.2 Two dimensional Flow on the Torus 187
8.3 Construction of the Flow and Invariant Measures 191
8.4 Invariant Densities 200
8.5 Statistical Solutions 203
8.6 Notes 205
Appendix 207
Bibliography 217
Notation 221
Index 225
|
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| author | Capiński, Marek 1951- Cutland, Nigel J. |
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| classification_rvk | SK 950 UF 4050 |
| ctrlnum | (OCoLC)31740152 (DE-599)BVBBV010497898 |
| dewey-full | 532/.58 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.58 |
| dewey-search | 532/.58 |
| dewey-sort | 3532 258 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV010497898 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T14:00:33Z |
| institution | BVB |
| isbn | 9810217102 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006995233 |
| oclc_num | 31740152 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-83 |
| owner_facet | DE-384 DE-703 DE-83 |
| physical | XII, 227 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | World Scientific |
| record_format | marc |
| series | Series on advances in mathematics for applied sciences |
| series2 | Series on advances in mathematics for applied sciences |
| spellingShingle | Capiński, Marek 1951- Cutland, Nigel J. Nonstandard methods for stochastic fluid mechanics Series on advances in mathematics for applied sciences Analyse mathématique non standard ram Fluides, mécanique des ram Processus stochastiques ram Fluid mechanics Nonstandard mathematical analysis Stochastic processes Hydromechanik (DE-588)4026312-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Nonstandard-Analysis (DE-588)4137021-1 gnd |
| subject_GND | (DE-588)4026312-5 (DE-588)4057630-9 (DE-588)4137021-1 |
| title | Nonstandard methods for stochastic fluid mechanics |
| title_auth | Nonstandard methods for stochastic fluid mechanics |
| title_exact_search | Nonstandard methods for stochastic fluid mechanics |
| title_full | Nonstandard methods for stochastic fluid mechanics Marek Capiński ; Nigel J. Cutland |
| title_fullStr | Nonstandard methods for stochastic fluid mechanics Marek Capiński ; Nigel J. Cutland |
| title_full_unstemmed | Nonstandard methods for stochastic fluid mechanics Marek Capiński ; Nigel J. Cutland |
| title_short | Nonstandard methods for stochastic fluid mechanics |
| title_sort | nonstandard methods for stochastic fluid mechanics |
| topic | Analyse mathématique non standard ram Fluides, mécanique des ram Processus stochastiques ram Fluid mechanics Nonstandard mathematical analysis Stochastic processes Hydromechanik (DE-588)4026312-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Nonstandard-Analysis (DE-588)4137021-1 gnd |
| topic_facet | Analyse mathématique non standard Fluides, mécanique des Processus stochastiques Fluid mechanics Nonstandard mathematical analysis Stochastic processes Hydromechanik Stochastischer Prozess Nonstandard-Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006995233&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004569239 |
| work_keys_str_mv | AT capinskimarek nonstandardmethodsforstochasticfluidmechanics AT cutlandnigelj nonstandardmethodsforstochasticfluidmechanics |