Stochastically forced compressible fluid flows:
Gespeichert in:
Hauptverfasser: | , , |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Berlin
De Gruyter
[2018]
|
Schriftenreihe: | De Gruyter Series in Applied and Numerical Mathematics
volume 3 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XII, 330 Seiten 24 cm x 17 cm, 712 g |
ISBN: | 9783110490503 9783110492569 |
Internformat
MARC
LEADER | 00000nam a2200000 cb4500 | ||
---|---|---|---|
001 | BV044745338 | ||
003 | DE-604 | ||
005 | 20181206 | ||
007 | t | ||
008 | 180202s2018 gw |||| 00||| eng d | ||
015 | |a 17,N25 |2 dnb | ||
016 | 7 | |a 1135496870 |2 DE-101 | |
020 | |a 9783110490503 |c Festeinband : EUR 99.95 (DE) (freier Preis), EUR 100.80 (AT) (freier Preis) |9 978-3-11-049050-3 | ||
020 | |a 9783110492569 |c Print + EBook |9 978-3-11-049256-9 | ||
024 | 3 | |a 9783110490503 | |
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041 | 0 | |a eng | |
044 | |a gw |c XA-DE-BE | ||
049 | |a DE-384 |a DE-634 |a DE-83 |a DE-M347 | ||
082 | 0 | |a 510 |2 23 | |
084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
084 | |a 76-02 |2 msc | ||
084 | |a 76N10 |2 msc | ||
084 | |a 76M35 |2 msc | ||
100 | 1 | |a Breit, Dominic |4 aut | |
245 | 1 | 0 | |a Stochastically forced compressible fluid flows |c Dominic Breit, Eduard Feireisl, Martina Hofmanová |
264 | 1 | |a Berlin |b De Gruyter |c [2018] | |
264 | 4 | |c © 2018 | |
300 | |a XII, 330 Seiten |c 24 cm x 17 cm, 712 g | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a De Gruyter Series in Applied and Numerical Mathematics |v volume 3 | |
650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Strömungsmechanik |0 (DE-588)4077970-1 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Navier-Stokes-Gleichung |0 (DE-588)4041456-5 |2 gnd |9 rswk-swf |
650 | 0 | 7 | |a Kompressible Strömung |0 (DE-588)4032018-2 |2 gnd |9 rswk-swf |
653 | |a Navier-Stokes-Gleichung | ||
653 | |a Fluiddynamik | ||
653 | |a Kompressible Strömung | ||
689 | 0 | 0 | |a Mathematische Physik |0 (DE-588)4037952-8 |D s |
689 | 0 | 1 | |a Strömungsmechanik |0 (DE-588)4077970-1 |D s |
689 | 0 | 2 | |a Kompressible Strömung |0 (DE-588)4032018-2 |D s |
689 | 0 | 3 | |a Navier-Stokes-Gleichung |0 (DE-588)4041456-5 |D s |
689 | 0 | |5 DE-604 | |
700 | 1 | |a Feireisl, Eduard |d 1957- |0 (DE-588)137457685 |4 aut | |
700 | 1 | |a Hofmanová, Martina |4 aut | |
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776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-049076-3 |
830 | 0 | |a De Gruyter Series in Applied and Numerical Mathematics |v volume 3 |w (DE-604)BV044780807 |9 3 | |
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999 | |a oai:aleph.bib-bvb.de:BVB01-030141118 |
Datensatz im Suchindex
_version_ | 1804178253506674688 |
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adam_text | CONTENTS
ACKNOWLEDGEMENTS* V
NOTATION * VII
PART I: PRELIMINARY RESULTS
1 ELEMENTS OF FUNCTIONAL ANALYSIS * 3
1.1 CONTINUOUS FUNCTIONS, MEASURES * 3
1.2 TOPOLOGICAL SPACES * 5
1.3 DIFFERENTIABLE FUNCTIONS, DISTRIBUTIONS * 6
1.4 INTEGRABLE FUNCTIONS * 7
1.5 COMPACTNESS AND CONVERGENCE OF INTEGRABLE FUNCTIONS *
1.6 SOBOLEV SPACES * 10
1.7 SOBOLEV SPACES OF PERIODIC FUNCTIONS * 12
1.7.1 HILBERTIAN STRUCTURE * 12
1.7.2
LP
-STRUCTURE * 13
1.7.3 REGULARIZATION BY CONVOLUTION KERNELS * 14
1.8 BOCHNER SPACES * 15
1.8.1 TIME REGULARITY * 15
1.8.2 COMPACT EMBEDDINGS * 16
1.8.3 REGULARIZATION BY CONVOLUTION KERNELS * 18
2 ELEMENTS OF STOCHASTIC ANALYSIS * 21
2.1 RANDOM VARIABLES AND STOCHASTIC PROCESSES * 21
2.2 RANDOM DISTRIBUTIONS * 30
2.2.1 MEASURABILITY * 31
2.2.2 REGULARIZATION * 32
2.2.3 EQUALITY IN LAW * 34
2.2.4 PROGRESSIVE MEASURABILITY * 36
2.2.5 SPECIAL CLASSES OF RANDOM DISTRIBUTIONS * 39
2.3 STOCHASTIC ITOE*S INTEGRAL * 40
2.4 IT6*S FORMULA * 46
2.5 PATHWISE VS. MARTINGALE SOLUTIONS * 47
2.5.1 PATHWISE UNIQUENESS VS. UNIQUENESS IN LAW * 49
2.6 STOCHASTIC COMPACTNESS METHOD * 50
2.7 JAKUBOWSKI-SKOROKHOD REPRESENTATION THEOREM *
2.8 RANDOM DISTRIBUTIONS IN
LP
AND YOUNG MEASURES *
2.9 STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS * 61
AN IN
2.10 GYOENGY-KRYLOV LEMMA * 66
2.11 S TATIONARY * 70
2.12 KRYLOV-BOGOLIUBOV METHOD * 74
PART II: EXISTENCE THEORY
3 MODELING FLUID MOTION SUBJECT TO RANDOM EFFECTS * 81
3.1 FIELD EQUATIONS * 82
3.1.1 CONSTITUTIVE RELATIONS - NAVIER-STOKES SYSTEM * 83
3.2 RANDOM PHENOMENA * 84
3.2.1 INITIAL DATA * 84
3.2.2 DRIVING FORCE * 86
3.3 STRONG PATHWISE SOLUTIONS * 88
3.4 DISSIPATIVE MARTINGALE SOLUTIONS * 90
3.4.1 WEAK FORMULATION * 92
3.4.2 REGULARITY PROPERTIES OF WEAK SOLUTIONS * 94
3.5 STATIONARY SOLUTIONS * 97
4 GLOBAL EXISTENCE * 101
4.1 SOLVABILITY OF THE BASIC APPROXIMATE PROBLEM * 107
4.1.1 ITERATION SCHEME * 108
4.1.2 THE LIMIT FOR VANISHING TIME STEP * 110
4.1.2.1 REGULARITY FOR THE VISCOUS APPROXIMATION OF THE EQUATION OF
CONTINUITY * 110
4.1.2.2 BOUNDS ON THE APPROXIMATE VELOCITIES * 111
4.1.2.3 HOELDER CONTINUITY OF APPROXIMATE VELOCITIES * 112
4.1.2.4 SOLVABILITY OF THE FIRST LEVEL APPROXIMATE PROBLEM * 113
4.1.3 PATHWISE UNIQUENESS * 117
4.1.4 STRONG SOLUTIONS * 121
4.1.5 GENERAL INITIAL DATA * 123
4.1.6 ENERGY BALANCE * 124
4.2 SOLVABILITY OF THE GALERKIN APPROXIMATION * 126
4.2.1 UNIFORM ENERGY BOUNDS * 128
4.2.2 PASSAGE TO THE LIMIT * 129
4.3 THE LIMIT IN THE GALERKIN APPROXIMATION SCHEME * 131
4.3.1 UNIFORM BOUNDS * 133
4.3.2 ASYMPTOTIC LIMIT * 135
4.4 VANISHING VISCOSITY LIMIT * 146
4.4.1 UNIFORM ENERGY BOUNDS * 148
4.4.2 PRESSURE ESTIMATES * 150
4.4.3 L IM ITE -* 0 * 153
4.4.3.1 STOCHASTIC COMPACTNESS METHOD * 155
4.4.32 DETERMINISTIC COMPACTNESS METHOD * 164
4.5 VANISHING ARTIFICIAL PRESSURE LIMIT * 169
4.5.1 UNIFORM ENERGY BOUNDS * 171
4.5.2 PRESSURE ESTIMATES * 172
4.5.3 LIMIT
OE
- 0 - STOCHASTIC COMPACTNESS METHOD * 175
4.5.4 LIMIT S - 0 -D E TE RM IN ISTIC COMPACTNESS METHOD * 181
4.5.4.1 COMPACTNESS OF THE DENSITY * 181
5 LOCAL WELL-POSEDNESS
* 187
5.1 PRELIMINARY CONSIDERATIONS * 191
5.1.1 REWRITING THE EQUATIONS AS A SYMMETRIC HYPERBOLIC-PARABOLIC
PROBLEM * 193
5.1.2 OUTLINE OF THE PROOF OF THEOREM 5.0.3 * 194
5.2 THE APPROXIMATE SYSTEM * 195
5.2.1 THE GALERKIN APPROXIMATION * 198
5.2.2 UNIFORM ESTIMATES * 200
5.2.3 COMPACTNESS * 204
5.2.4 IDENTIFICATION OF THE LIMIT * 206
5.2.5 PATHWISE UNIQUENESS
-----
207
5.2.6 EXISTENCE OF A STRONG PATHWISE APPROXIMATE SOLUTION * 209
5.3 PROOF OF THEOREM 5.0.3 * 211
5.3.1 UNIQUENESS * 211
5.3.2 EXISTENCE OF A LOCAL STRONG SOLUTION FOR BOUNDED INITIAL DATA *
212
5.3.3 EXISTENCE OF A LOCAL STRONG SOLUTION FOR GENERAL INITIAL DATA *
213
5.3.4 EXISTENCE OF A MAXIMAL STRONG SOLUTION * 214
6 RELATIVE ENERGY INEQUALITY AND WEAK-STRONG UNIQUENESS * 217
6.1 RELATIVE ENERGY INEQUALITY* 220
6.2 WEAK-STRONG UNIQUENESS * 223
6.2.1 PATHWISE WEAK-STRONG UNIQUENESS * 224
6.2.2 WEAK-STRONG UNIQUENESS IN LAW * 228
PART III: APPLICATIONS
7 STATIONARY SOLUTIONS * 235
7.1 BASIC FINITE-DIMENSIONAL APPROXIMATION * 240
7.1.1 APPROXIMATE FIELD EQUATIONS * 240
7.1.2 BASIC ENERGY ESTIMATES * 241
7.1.3 REGULARITY OF THE DENSITY * 244
7.1.4 APPROXIMATE INVARIANT MEASURES * 246
7.2 FIRST LIMIT PROCEDURES: /? -
OO,
M -
OO
* 250
7.3 VANISHING VISCOSITY LIMIT * 255
7.4 VANISHING ARTIFICIAL PRESSURE LIMIT * 266
8 SINGULAR LIMITS * 271
8.1 INCOMPRESSIBLE LIMIT * 273
8.1.1 INCOMPRESSIBLE NAVIER-STOKES EQUATIONS * 275
8.1.2 MAIN RESULT * 278
8.1.3 CONVERGENCE IN LAW - THE PROOF OF THEOREM 8.1.6 * 280
8.1.3.1 UNIFORM BOUNDS * 280
8.1.3.2 ACOUSTIC EQUATION * 284
8.1.3.3 COMPACTNESS * 285
8.1.3.4 IDENTIFICATION OF THE LIMIT * 289
8.1.4 CONVERGENCE IN PROBABILITY - THE PROOF OF THEOREM 8.1.7 * 295
8.2 INVISCID-INCOMPRESSIBLE LIMIT * 297
8.2.1 SOLUTIONS OF THE EULER SYSTEM * 298
8.2.2 MAIN RESULT * 300
8.2.3 PROOF OF THEOREM 8.2.4 * 302
A APPENDIX * 305
A .L ELLIPTIC EQUATIONS AND RELATED PROBLEMS * 305
A.2 REGULARITY FOR PARABOLIC EQUATIONS * 309
A.3 RENORMALIZED SOLUTIONS OF THE CONTINUITY EQUATION * 312
A.4 A GENERALIZED LTD FORMULA * 313
B BIBLIOGRAPHICAL REMARKS
* 317
BIBLIOGRAPHY* 319
INDEX * 327
|
any_adam_object | 1 |
author | Breit, Dominic Feireisl, Eduard 1957- Hofmanová, Martina |
author_GND | (DE-588)137457685 |
author_facet | Breit, Dominic Feireisl, Eduard 1957- Hofmanová, Martina |
author_role | aut aut aut |
author_sort | Breit, Dominic |
author_variant | d b db e f ef m h mh |
building | Verbundindex |
bvnumber | BV044745338 |
classification_rvk | SK 950 |
ctrlnum | (OCoLC)1026336039 (DE-599)DNB1135496870 |
dewey-full | 510 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 510 - Mathematics |
dewey-raw | 510 |
dewey-search | 510 |
dewey-sort | 3510 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Book |
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id | DE-604.BV044745338 |
illustrated | Not Illustrated |
indexdate | 2024-07-10T08:01:02Z |
institution | BVB |
institution_GND | (DE-588)10095502-2 |
isbn | 9783110490503 9783110492569 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030141118 |
oclc_num | 1026336039 |
open_access_boolean | |
owner | DE-384 DE-634 DE-83 DE-M347 |
owner_facet | DE-384 DE-634 DE-83 DE-M347 |
physical | XII, 330 Seiten 24 cm x 17 cm, 712 g |
publishDate | 2018 |
publishDateSearch | 2018 |
publishDateSort | 2018 |
publisher | De Gruyter |
record_format | marc |
series | De Gruyter Series in Applied and Numerical Mathematics |
series2 | De Gruyter Series in Applied and Numerical Mathematics |
spelling | Breit, Dominic aut Stochastically forced compressible fluid flows Dominic Breit, Eduard Feireisl, Martina Hofmanová Berlin De Gruyter [2018] © 2018 XII, 330 Seiten 24 cm x 17 cm, 712 g txt rdacontent n rdamedia nc rdacarrier De Gruyter Series in Applied and Numerical Mathematics volume 3 Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Kompressible Strömung (DE-588)4032018-2 gnd rswk-swf Navier-Stokes-Gleichung Fluiddynamik Kompressible Strömung Mathematische Physik (DE-588)4037952-8 s Strömungsmechanik (DE-588)4077970-1 s Kompressible Strömung (DE-588)4032018-2 s Navier-Stokes-Gleichung (DE-588)4041456-5 s DE-604 Feireisl, Eduard 1957- (DE-588)137457685 aut Hofmanová, Martina aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-049255-2 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-049076-3 De Gruyter Series in Applied and Numerical Mathematics volume 3 (DE-604)BV044780807 3 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030141118&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Breit, Dominic Feireisl, Eduard 1957- Hofmanová, Martina Stochastically forced compressible fluid flows De Gruyter Series in Applied and Numerical Mathematics Mathematische Physik (DE-588)4037952-8 gnd Strömungsmechanik (DE-588)4077970-1 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Kompressible Strömung (DE-588)4032018-2 gnd |
subject_GND | (DE-588)4037952-8 (DE-588)4077970-1 (DE-588)4041456-5 (DE-588)4032018-2 |
title | Stochastically forced compressible fluid flows |
title_auth | Stochastically forced compressible fluid flows |
title_exact_search | Stochastically forced compressible fluid flows |
title_full | Stochastically forced compressible fluid flows Dominic Breit, Eduard Feireisl, Martina Hofmanová |
title_fullStr | Stochastically forced compressible fluid flows Dominic Breit, Eduard Feireisl, Martina Hofmanová |
title_full_unstemmed | Stochastically forced compressible fluid flows Dominic Breit, Eduard Feireisl, Martina Hofmanová |
title_short | Stochastically forced compressible fluid flows |
title_sort | stochastically forced compressible fluid flows |
topic | Mathematische Physik (DE-588)4037952-8 gnd Strömungsmechanik (DE-588)4077970-1 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Kompressible Strömung (DE-588)4032018-2 gnd |
topic_facet | Mathematische Physik Strömungsmechanik Navier-Stokes-Gleichung Kompressible Strömung |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030141118&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV044780807 |
work_keys_str_mv | AT breitdominic stochasticallyforcedcompressiblefluidflows AT feireisleduard stochasticallyforcedcompressiblefluidflows AT hofmanovamartina stochasticallyforcedcompressiblefluidflows AT walterdegruytergmbhcokg stochasticallyforcedcompressiblefluidflows |