Asymptotic behavior of dynamical systems in fluid mechanics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Springfield, MO
American Inst. of Math. Sciences
2010
|
| Schriftenreihe: | AIMS on applied mathematics
4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 298 S. |
| ISBN: | 9781601330031 1601330030 |
Internformat
MARC
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| 020 | |a 1601330030 |9 1-60133-003-0 | ||
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| 035 | |a (DE-599)BVBBV036457984 | ||
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| 100 | 1 | |a Feireisl, Eduard |d 1957- |e Verfasser |0 (DE-588)137457685 |4 aut | |
| 245 | 1 | 0 | |a Asymptotic behavior of dynamical systems in fluid mechanics |c Eduard Feireisl and Dalibor Pražák |
| 264 | 1 | |a Springfield, MO |b American Inst. of Math. Sciences |c 2010 | |
| 300 | |a XII, 298 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a AIMS on applied mathematics |v 4 | |
| 650 | 0 | 7 | |a Strömungsmechanik |0 (DE-588)4077970-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Methode |0 (DE-588)4155620-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Navier-Stokes-Gleichung |0 (DE-588)4041456-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Navier-Stokes-Gleichung |0 (DE-588)4041456-5 |D s |
| 689 | 0 | 2 | |a Mathematische Methode |0 (DE-588)4155620-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Pražák, Dalibor |e Verfasser |0 (DE-588)133466779 |4 aut | |
| 830 | 0 | |a AIMS on applied mathematics |v 4 |w (DE-604)BV023094684 |9 4 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020329937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020329937 | ||
Datensatz im Suchindex
| _version_ | 1804142948030349312 |
|---|---|
| adam_text | Contents
Preliminaries
.............................................. 1
1.1 Notation............................................... 1
1.1.1 Symbols.......................................... 1
1.1.2
Euclidean space
................................... 1
1.1.3
Norms
........................................... 2
1.1.4
Differential operators
.............................. 3
1.2
Measures and distributions
............................... 4
1.2.1
Continuously differentiable functions
................. 4
1.2.2
Compactness of sets of continuous functions
.......... 5
1.2.3
Measures
......................................... 6
1.2.4
Distributions
..................................... 7
1.3
Bochner and Sobolev spaces
.............................. 7
1.3.1
Lebesgue (Bochner) spaces
......................... 7
1.3.2
Sobolev spaces
.................................... 10
1.3.3
Dual Sobolev spaces
............................... 10
1.3.4
Embeddings for dual Sobolev spaces
................. 12
1.3.5
Traces
........................................... 12
1.3.6
Interpolation
...................................... 14
1.4
Fourier analysis
......................................... 14
1.4.1
Fourier transform of tempered distributions
........... 15
1.4.2
Boundedness of Fourier multipliers
.................. 16
1.5
Compactness of families of functions
....................... 17
1.5.1
Weak compactness of
integrable
functions
............ 17
1.5.2
Young measures
................................... 18
1.6
Gronwall s lemma
....................................... 19
Dynamical systems
........................................ 21
2.1
Dynamical systems and attractors
......................... 22
2.2
Fractal dimension
....................................... 27
2.3
Exponential attractor
.................................... 29
2.4
Method of trajectories
................................... 36
X
Contents
2.5
Method of Lyapunov exponents
........................... 43
2.5.1
Coverings of ellipsoids
.............................. 45
2.5.2
Lyapunov exponents and solution operators
........... 48
2.6
Extension to the case without uniqueness
................... 53
2.7
Bibliographical remarks
................................... 56
3
Viscous fluid systems
...................................... 59
3.1
Fields and balance laws
.................................. 59
3.1.1
Balance law
-
integral formulation
................... 61
3.1.2
Balance law
-
formal interpretation
.................. 64
3.1.3
Weak sequential stability
........................... 65
3.2
Kinematics of mass transport
............................. 65
3.2.1
Renormalization
................................... 66
3.3
Momentum equation
..................................... 70
3.4
Total energy balance
..................................... 71
3.4.1
Kinetic and internal energy balance
.................. 72
3.4.2
Conservative boundary conditions and the total
energy balance
.................................... 72
3.5
Entropy
................................................ 73
3.5.1
Entropy production as
a non-
negative Radon measure
.. 74
3.6
Fluid description
........................................ 76
3.6.1
General constitutive relations
....................... 76
3.6.2
Navier-Stokes-Fourier system
....................... 77
3.7
Constitutive equations
................................... 81
3.7.1
Hypothesis of thermodynamic stability
............... 82
3.7.2
Monoatomic gas state equation
...................... 82
3.7.3
Third law of thermodynamics, entropy
............... 83
3.7.4
Radiation
........................................ 84
3.7.5
Transport coefficients
.............................. 85
4
Complete fluid systems, analysis
........................... 87
4.1
Equilibrium states
....................................... 88
4.1.1
Total mass conservation
............................ 88
4.1.2
Total dissipation balance
........................... 88
4.1.3
Static states
...................................... 90
4.2
Weak sequential stability
................................. 94
4.2.1
Stability of solutions under a uniform energy bound
... 95
4.3
Global-in-time solutions
..................................117
4.3.1
Existence theory
..................................117
4.4
Long-time behavior of conservative systems
.................120
5
Large time behavior
.......................................125
5.1
Large time behavior revisited
.............................127
5.1.1
Uniform decay of density oscillations
.................129
5.2
Energy blow up
.......................................138
Contents
XI
5.2.1
A general result
...................................138
5.2.2
Applications
......................................143
5.3
Rapidly oscillating driving forces
..........................146
5.3.1
Energy estimates
..................................149
5.3.2
Uniform bounds via iteration
.......................151
5.3.3
Convergence
......................................152
5.3.4
Concluding remarks
...............................153
6
Complete and simplified fluid systems
.....................155
6.1
Dynamical systems approach
..............................156
6.1.1
Dissipativity
......................................157
6.1.2
Global trajectories and attractors
...................158
6.2
Dynamics of reduced systems
.............................159
6.2.1
Barotropic compressible fluids
.......................161
6.2.2
Incompressible fluids
...............................162
6.3
Bibliographical comments
................................165
7
Incompressible model of Ladyzhenskaya
...................169
7.1
Statement of the problem
.................................170
7.1.1
Assumptions on the stress tensor
....................171
7.1.2
Mathematical formulation of the problem
.............173
7.1.3
Existence and uniqueness results
....................175
7.2
2D Navier-Stokes equations
...............................180
7.2.1
Dissipativity and absorbing set
......................181
7.2.2
Differentiability of the solution operator
..............183
7.2.3
Estimates of the trace. Attractor dimension
...........184
7.3
2D Ladyzhenskaya model; case
r
> 2.......................187
7.3.1
Dissipativity and absorbing set
......................188
7.3.2
Differentiability of the solution semigroup
............190
7.3.3
Estimates of the trace. Attractor dimension
...........192
7.4 3D
Ladyzhenskaya model; case
r
> 11/5 ...................194
7.4.1
Existence of exponential attractor
...................195
7.4.2
Explicit dimension estimates for
r
> 12/5 ............203
8
2D Model of Ladyzhenskaya for
г
< 2 .....................217
8.1
2D Ladyzhenskaya model; case
r
Є
(1,2) ...................218
8.1.1
Basic mathematical theory
.........................218
8.1.2
Dissipativity and the dynamics of trajectories
.........224
8.1.3
Exponential attractor
..............................226
8.1.4
Improved estimates for
r
> 4/3......................234
8.2
Fluids with pressure-dependent viscosities
..................238
8.2.1
Basic mathematical theory
.........................241
8.2.2
Dissipativity and absorbing set
......................246
8.2.3
Existence of exponential attractor
...................251
8.3
Bibliographical remarks
..................................257
XII Contents
9 Appendix..................................................259
9.1 Embeddings and
interpolations
............................259
9.2 Korn and
Poincaré
type inequalities
.......................262
9.3 Div-Curl
lemma and related topics.........................
264
9.4
A result of P.-L. Lions on weak continuity
..................268
9.5
Coverings of compacts in Bochner spaces
....................272
9.5.1
Bochner spaces
....................................272
9.5.2
Asymptotics of the sequences
.......................276
9.5.3
Aubin-Lions
lemma
................................277
9.6
Lieb-Thirring inequality
..................................281
9.7
Properties of the stress tensor
.............................283
References
.....................................................285
Index
..........................................................295
|
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| author | Feireisl, Eduard 1957- Pražák, Dalibor |
| author_GND | (DE-588)137457685 (DE-588)133466779 |
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| id | DE-604.BV036457984 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:39:52Z |
| institution | BVB |
| isbn | 9781601330031 1601330030 |
| language | English |
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| physical | XII, 298 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | American Inst. of Math. Sciences |
| record_format | marc |
| series | AIMS on applied mathematics |
| series2 | AIMS on applied mathematics |
| spelling | Feireisl, Eduard 1957- Verfasser (DE-588)137457685 aut Asymptotic behavior of dynamical systems in fluid mechanics Eduard Feireisl and Dalibor Pražák Springfield, MO American Inst. of Math. Sciences 2010 XII, 298 S. txt rdacontent n rdamedia nc rdacarrier AIMS on applied mathematics 4 Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Navier-Stokes-Gleichung (DE-588)4041456-5 s Mathematische Methode (DE-588)4155620-3 s DE-604 Pražák, Dalibor Verfasser (DE-588)133466779 aut AIMS on applied mathematics 4 (DE-604)BV023094684 4 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020329937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Feireisl, Eduard 1957- Pražák, Dalibor Asymptotic behavior of dynamical systems in fluid mechanics AIMS on applied mathematics Strömungsmechanik (DE-588)4077970-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4155620-3 (DE-588)4041456-5 |
| title | Asymptotic behavior of dynamical systems in fluid mechanics |
| title_auth | Asymptotic behavior of dynamical systems in fluid mechanics |
| title_exact_search | Asymptotic behavior of dynamical systems in fluid mechanics |
| title_full | Asymptotic behavior of dynamical systems in fluid mechanics Eduard Feireisl and Dalibor Pražák |
| title_fullStr | Asymptotic behavior of dynamical systems in fluid mechanics Eduard Feireisl and Dalibor Pražák |
| title_full_unstemmed | Asymptotic behavior of dynamical systems in fluid mechanics Eduard Feireisl and Dalibor Pražák |
| title_short | Asymptotic behavior of dynamical systems in fluid mechanics |
| title_sort | asymptotic behavior of dynamical systems in fluid mechanics |
| topic | Strömungsmechanik (DE-588)4077970-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| topic_facet | Strömungsmechanik Mathematische Methode Navier-Stokes-Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020329937&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023094684 |
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