Asymptotic stability of steady compressible fluids:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Lecture notes in mathematics
2024 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIV, 235 S. |
| ISBN: | 3642211364 9783642211362 |
Internformat
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
TOPICS IN FLUID MECHANICS 1
1.1 INTRODUCTION 1
1.2 MATHEMATICAL NOTATIONS 2
1.2.1 GEOMETRICAL NOTATIONS 2
1.2.2 ANALYTICAL NOTATIONS 5
1.3 KINEMATICS 9
1.3.1 VECTORIAL NOTATIONS 10
1.3.2 EULERIAN AND LAGRANGEAN DESCRIPTIONS 11
1.3.3 REYNOLDS TRANSPORT THEOREM 11
1.3.4 FRAMES 13
1.3.5 FROM MACROSCOPIC TO LOCAL LAWS 14
1.3.6 MASS, MOMENTUM, ROTATIONAL MOMENTUM, KINETIC ENERGY 14
1.4 MECHANICS 15
1.4.1 FORCES 16
1.4.2 CONSERVATION OF MASS 17
1.4.3 BALANCE LAWS OF MOMENTUM, ROTATIONAL MOMENTUM. 18 1.4.4 STRESS
TENSOR 19
1.4.5 BALANCE EQUATIONS IN LOCAL FORM 20
1.4.6 INCOMPRESSIBLE EULER EQUATIONS 21
1.4.7 CONSTITUTIVE EQUATIONS 22
1.4.8 LINEARLY VISCOUS FLUIDS 23
1.5 THERMODYNAMICS 25
1.5.1 THERMODYNAMICAL VARIABLES 25
1.5.2 THE FIRST LAW OF THERMODYNAMICS 27
1.5.3 THE SECOND LAW OF THERMODYNAMICS 29
1.5.4 CLAUSIUS-DUHEM INEQUALITY 30
1.5.5 PHENOMENOLOGICAL LAWS 32
1.5.6 COMPRESSIBLE EULER EQUATIONS 33
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1011288451
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
1.5.7 LINEARLY VISCOUS FLUIDS 34
1.5.8 HEAT-CONDUCTING FLUIDS 35
1.6 SIDE CONDITIONS 36
1.6.1 CLASSES OF BOUNDARY CONDITIONS 37
1.6.2 BOUNDARY CONDITIONS ON VELOCITY 38
1.6.3 BOUNDARY CONDITIONS ON STRESS 40
1.6.4 BOUNDARY CONDITIONS ON TEMPERATURE 43
1.6.5 SIDE CONDITIONS ON DENSITY 44
1.7 THREE MODEL PROBLEMS 46
1.7.1 INCOMPRESSIBLE FLUIDS 47
1.7.2 BAROTROPIC FLUIDS 48
1.7.3 POLYTROPIC FLUIDS 50
1.7.4 BIBLIOGRAPHICAL NOTES 51
TOPICS IN STABILITY 53
2.1 INTRODUCTION 53
2.2 NONLINEAR STABILITY 54
2.2.1 ABSTRACT SETTINGS 55
2.2.2 INITIAL DATA CONTROL 58
2.2.3 LYAPUNOV METHOD 59
2.2.4 ENERGY METHOD 60
2.3 LAGRANGE-DIRICHLET METHOD 62
2.3.1 HYPERBOLIC FIRST ORDER SYSTEMS 62
2.3.2 SECOND ORDER ODE 64
2.3.3 STABILITY OF BAROTROPIC INVISCID FLUIDS V 6 ^ 0 66
2.3.4 ISOTHERMAL VISCOUS FLUIDS V 6 = 0 71
2.4 MAIN THEOREMS 74
2.4.1 CASE (A) BAROTROPIC FLUID, RIGID BOUNDARY 74
2.4.2 CASE (B) ISOTHERMAL FLUID, DEFORMABLE BOUNDARY 80 2.4.3 CASE (C)
POLYTROPIC FLUID, RIGID BOUNDARY 85
2.5 BIBLIOGRAPHICAL NOTES 86
BAROTROPIC FLUIDS WITH RIGID BOUNDARY 87
3.1 INTRODUCTION 87
3.2 Q BOUNDED, POTENTIAL FORCES 89
3.2.1 UNIQUENESS OF THE REST STATE 90
3.2.2 NONLINEAR STABILITY 91
3.2.3 NONLINEAR EXPONENTIAL STABILITY 96
3.3 UE BOUNDED, NON-POTENTIAL FORCES 100
3.3.1 UNIQUENESS / ^ VC/ 100
3.3.2 NONLINEAR STABILITY 106
3.3.3 NONLINEAR EXPONENTIAL STABILITY 109
3.4 FT BOUNDED, NON ZERO BOUNDARY DATA 113
3.4.1 UNIQUENESS 113
3.4.2 NONLINEAR EXPONENTIAL STABILITY 115
IMAGE 3
CONTENTS
3.5 CL EXTERIOR, FIXED COMPACT REGION 116
3.5.1 UNIQUENESS 117
3.5.2 NONLINEAR EXPONENTIAL STABILITY 119
3.6 INSTABILITY 122
3.7 AUXILIARY LEMMAS 126
3.7.1 FUNCTION V FOR UNIQUENESS 126
3.7.2 FUNCTION V FOR STABILITY 128
3.7.3 BIBLIOGRAPHICAL NOTES 131
ISOTHERMAL FLUIDS WITH FREE BOUNDARIES 133
4.1 INTRODUCTION 133
4.2 POSITION OF THE PROBLEM 136
4.2.1 GEOMETRICAL TOOLS 136
4.2.2 EQUATIONS OF MOTION 138
4.2.3 REST STATE AND EQUILIBRIUM CONFIGURATIONS 139
4.2.4 FIRST AND SECOND VARIATIONS OF ENERGY 141
4.3 DEFINITIONS RELATED TO STABILITY 147
4.3.1 INITIAL DATA CONTROL 149
4.3.2 PRESENT RESULTS 152
4.4 UNIQUENESS 154
4.5 NONLINEAR STABILITY 158
4.5.1 ENERGY EQUATION 158
4.5.2 NONLINEAR STABILITY 162
4.5.3 NONLINEAR EXPONENTIAL STABILITY 164
4.6 LOSS OF STABILITY 171
4.6.1 ENERGY INEQUALITY 171
4.6.2 EQUIVALENCE OF NORMS 173
4.6.3 INSTABILITY 175
4.6.4 LOSS OF INITIAL DATA CONTROL 179
4.7 SIGN OF EO IN TERMS OF SIZE OF PERTURBATION 179
4.7.1 PROOF OF THEOREM 4.7.1 180
4.7.2 PROOF OF THEOREM 4.7.2 183
4.8 AUXILIARY LEMMAS 187
4.8.1 FUNCTION V FOR UNIQUENESS 187
4.8.2 FUNCTIONS V FOR STABILITY AND INSTABILITY 190
4.8.3 BIBLIOGRAPHICAL NOTES 194
POLYTROPIC FLUIDS WITH RIGID BOUNDARY 197
5.1 INTRODUCTION 197
5.1.1 EQUATIONS OF MOTION 198
5.2 UNIQUENESS OF THE REST STATE 201
5.3 STABILITY PROBLEM 207
5.3.1 ENERGY EQUATION 208
5.3.2 ENERGY EQUATION OF PERTURBATION 209
5.3.3 NONLINEAR EXPONENTIAL STABILITY 213
IMAGE 4
XIV CONTENTS
5.4 AUXILIARY LEMMAS 217
5.4.1 SOME INEQUALITIES 217
5.4.2 FUNCTION V FOR UNIQUENESS 218
5.4.3 AUXILIARY FUNCTION FOR STABILITY 219
5.4.4 BIBLIOGRAPHICAL NOTES 221
BIBLIOGRAPHY 223
INDEX 231 |
| any_adam_object | 1 |
| author | Padula, Mariarosaria -2012 |
| author_GND | (DE-588)132344378 |
| author_facet | Padula, Mariarosaria -2012 |
| author_role | aut |
| author_sort | Padula, Mariarosaria -2012 |
| author_variant | m p mp |
| building | Verbundindex |
| bvnumber | BV039566572 |
| classification_rvk | SI 850 |
| classification_tum | MAT 356f MAT 357f PHY 227f |
| ctrlnum | (OCoLC)752226974 (DE-599)DNB1011288451 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV039566572 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-21T00:09:16Z |
| institution | BVB |
| isbn | 3642211364 9783642211362 |
| language | English |
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| physical | XIV, 235 S. |
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| series2 | Lecture notes in mathematics |
| spelling | Padula, Mariarosaria -2012 Verfasser (DE-588)132344378 aut Asymptotic stability of steady compressible fluids Mariarosaria Padula Berlin [u.a.] Springer 2011 XIV, 235 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2024 Ljapunov-Methode (DE-588)4167990-8 gnd rswk-swf Parabolisches Differentialgleichungssystem (DE-588)4833677-4 gnd rswk-swf Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd rswk-swf Kompressible Strömung (DE-588)4032018-2 gnd rswk-swf Stationäre Strömung (DE-588)4132826-7 gnd rswk-swf Kompressible Strömung (DE-588)4032018-2 s Stationäre Strömung (DE-588)4132826-7 s Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 s Parabolisches Differentialgleichungssystem (DE-588)4833677-4 s Ljapunov-Methode (DE-588)4167990-8 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-21137-9 Lecture notes in mathematics 2024 (DE-604)BV000676446 2024 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3713542&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024418158&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Padula, Mariarosaria -2012 Asymptotic stability of steady compressible fluids Lecture notes in mathematics Ljapunov-Methode (DE-588)4167990-8 gnd Parabolisches Differentialgleichungssystem (DE-588)4833677-4 gnd Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd Kompressible Strömung (DE-588)4032018-2 gnd Stationäre Strömung (DE-588)4132826-7 gnd |
| subject_GND | (DE-588)4167990-8 (DE-588)4833677-4 (DE-588)4496581-3 (DE-588)4032018-2 (DE-588)4132826-7 |
| title | Asymptotic stability of steady compressible fluids |
| title_auth | Asymptotic stability of steady compressible fluids |
| title_exact_search | Asymptotic stability of steady compressible fluids |
| title_full | Asymptotic stability of steady compressible fluids Mariarosaria Padula |
| title_fullStr | Asymptotic stability of steady compressible fluids Mariarosaria Padula |
| title_full_unstemmed | Asymptotic stability of steady compressible fluids Mariarosaria Padula |
| title_short | Asymptotic stability of steady compressible fluids |
| title_sort | asymptotic stability of steady compressible fluids |
| topic | Ljapunov-Methode (DE-588)4167990-8 gnd Parabolisches Differentialgleichungssystem (DE-588)4833677-4 gnd Hyperbolisches Differentialgleichungssystem (DE-588)4496581-3 gnd Kompressible Strömung (DE-588)4032018-2 gnd Stationäre Strömung (DE-588)4132826-7 gnd |
| topic_facet | Ljapunov-Methode Parabolisches Differentialgleichungssystem Hyperbolisches Differentialgleichungssystem Kompressible Strömung Stationäre Strömung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3713542&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024418158&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT padulamariarosaria asymptoticstabilityofsteadycompressiblefluids |