SPDE in hydrodynamic: recent progress and prospects: lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Schriftenreihe: | Lecture notes in mathematics
1942 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 166 S. 235 mm x 155 mm |
| ISBN: | 9783540784920 3540784926 |
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| 245 | 1 | 0 | |a SPDE in hydrodynamic: recent progress and prospects |b lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005 |c Sergio Albeverio ; Franco Flandoli ; Yakov G. Sinai. Ed.: Giuseppe Da Prato ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a VIII, 166 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1942 | |
| 650 | 4 | |a Analyse dimensionnelle - Congrès | |
| 650 | 4 | |a Fluides, Dynamique des - Modèles mathématiques - Congrès | |
| 650 | 4 | |a Hydrodynamique - Congrès | |
| 650 | 4 | |a Hydrodynamique - Modèles mathématiques - Congrès | |
| 650 | 4 | |a Navier-Stokes, Équations de - Solutions numériques - Congrès | |
| 650 | 4 | |a Processus stochastiques - Congrès | |
| 650 | 4 | |a Mathematisches Modell | |
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| 650 | 4 | |a Fluid dynamics |x Mathematical models |v Congresses | |
| 650 | 4 | |a Hydrodynamics |v Congresses | |
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Datensatz im Suchindex
| _version_ | 1804137619079036928 |
|---|---|
| adam_text | Contents
Some Methods of Infinite Dimensional Analysis
in Hydrodynamics: An Introduction
Sergio
Albeveño
and
Benedetta Ferrano
............................ 1
1
Introduction
.................................................. 1
2
The
Euler
Equation, its Invariants and Associated
Invariant Measures
............................................ 2
2.1
The
Euler
Equation
....................................... 2
2.2
The
Euler
Equation in Terms of Vorticity
.................... 3
2.3
The Conserved Quantities for the
Euler
Equation
............. 4
2.4
Heuristic Invariant Measures Associated
with the
Euler
Equation
................................... 6
2.5
The
Euler
Equation in Terms of the Fourier Components
of the Stream Function
..................................... 8
2.6
The Necessity of Looking for Singular Solutions. Divergence
of the Energy with Respect to the Enstrophy Measure
......... 9
2.7
Relation of the Enstrophy Measure
μΊ
with the
Euler
Equation
................................... 10
2.8
The Infinitesimal
Invariance
of
μΊ.
Relation with the
Hopf
Approach
............................................... 11
2.9
The Question of Uniqueness of Generators of the
Euler
Flow
.... 12
2.10
An
Euler
Flow in a Sobolev Space of Negative Index
........... 14
2.11
Some Remarks on the Vortex Model and its Relations
with the
Euler
Equation
................................... 14
3
Stochastic Navier-Stokes Equation
.............................. 16
3.1
The Navier-Stokes Equation with Space-Time White Noise
..... 17
3.2
The Gaussian Invariant Measure Given by the Enstrophy
(and the Viscosity Parameter)
.....,........,...........----- 20
3.3
Existence of Strong Solutions
............................... 23
3.4
Pathwise Uniqueness
....................................... 29
3.5
Some Additional Remarks and Complements
.......-......... 33
3.6
Appendix
................................................ 35
References
........................-............................. 36
VIII Contents
An Introduction
to
3D
Stochastic Fluid Dynamics
Franco Flandoli
.................................................. 51
1
Introduction
.................................................. 51
2
Abstract Framework and General Preliminaries
................... 52
3
Finite Dimensional Models
..................................... 57
3.1
Introduction and Examples
................................. 57
3.2
A Priori Bounds
.......................................... 60
3.3
Comparison of Two Solutions and Pathwise Estimates
......... 71
3.4
Existence and Uniqueness, Markov Property
.................. 73
3.5
Invariant Measures
........................................ 75
3.6
Galerkin Stationary Measures for the
3D
Equation
............ 79
4
Stochastic Navier-Stokes Equations in
3D........................ 82
4.1
Concepts of Solution
....................................... 82
4.2
Existence of Solutions to the Martingale Problem
............. 86
4.3
Technical Complements
.................................... 91
4.4
An Abstract Markov Selection Result
........................ 95
4.5
Markov Selection for the
3D
Stochastic NSE s
.................103
4.6
Continuity in
«о
of Markov Solutions
........................109
5
Some Topics on Turbulence
.....................................124
5.1
Introduction and a Few Keywords
...........................124
5.2
K41 Scaling Law: Heuristics and Unclear Issues
...............126
5.3
Definitions and Examples
..................................129
5.4
Brownian Eddies and Random Vortex Filaments
..............133
5.5
Necessary Conditions for K41
...............................139
5.6
A Condition Equivalent to K41
.............................144
References
......................................................148
Mathematical Results Related to the
Navier—
Stokes System
Yakov G. Sinai
..................................................151
1
Introduction
..................................................151
2
Power Series and Diagrams for the Navier-Stokes-System
...........154
3
Foias-Temam Theorem for 2.0-Navier-Stokes System with Periodic
Boundary Condition
...........................................158
4
Burgers System and
1-
D Inviscid
Burgers Equation
with Random Forcing
..........................................161
References
......................................................163
List of Participants
............................................165
|
| adam_txt |
Contents
Some Methods of Infinite Dimensional Analysis
in Hydrodynamics: An Introduction
Sergio
Albeveño
and
Benedetta Ferrano
. 1
1
Introduction
. 1
2
The
Euler
Equation, its Invariants and Associated
Invariant Measures
. 2
2.1
The
Euler
Equation
. 2
2.2
The
Euler
Equation in Terms of Vorticity
. 3
2.3
The Conserved Quantities for the
Euler
Equation
. 4
2.4
Heuristic Invariant Measures Associated
with the
Euler
Equation
. 6
2.5
The
Euler
Equation in Terms of the Fourier Components
of the Stream Function
. 8
2.6
The Necessity of Looking for Singular Solutions. Divergence
of the Energy with Respect to the Enstrophy Measure
. 9
2.7
Relation of the Enstrophy Measure
μΊ
with the
Euler
Equation
. 10
2.8
The Infinitesimal
Invariance
of
μΊ.
Relation with the
"Hopf
Approach"
. 11
2.9
The Question of Uniqueness of Generators of the
Euler
Flow
. 12
2.10
An
Euler
Flow in a Sobolev Space of Negative Index
. 14
2.11
Some Remarks on the Vortex Model and its Relations
with the
Euler
Equation
. 14
3
Stochastic Navier-Stokes Equation
. 16
3.1
The Navier-Stokes Equation with Space-Time White Noise
. 17
3.2
The Gaussian Invariant Measure Given by the Enstrophy
(and the Viscosity Parameter)
.,.,.----- 20
3.3
Existence of Strong Solutions
. 23
3.4
Pathwise Uniqueness
. 29
3.5
Some Additional Remarks and Complements
.-. 33
3.6
Appendix
. 35
References
.-. 36
VIII Contents
An Introduction
to
3D
Stochastic Fluid Dynamics
Franco Flandoli
. 51
1
Introduction
. 51
2
Abstract Framework and General Preliminaries
. 52
3
Finite Dimensional Models
. 57
3.1
Introduction and Examples
. 57
3.2
A Priori Bounds
. 60
3.3
Comparison of Two Solutions and Pathwise Estimates
. 71
3.4
Existence and Uniqueness, Markov Property
. 73
3.5
Invariant Measures
. 75
3.6
Galerkin Stationary Measures for the
3D
Equation
. 79
4
Stochastic Navier-Stokes Equations in
3D. 82
4.1
Concepts of Solution
. 82
4.2
Existence of Solutions to the Martingale Problem
. 86
4.3
Technical Complements
. 91
4.4
An Abstract Markov Selection Result
. 95
4.5
Markov Selection for the
3D
Stochastic NSE's
.103
4.6
Continuity in
«о
of Markov Solutions
.109
5
Some Topics on Turbulence
.124
5.1
Introduction and a Few Keywords
.124
5.2
K41 Scaling Law: Heuristics and Unclear Issues
.126
5.3
Definitions and Examples
.129
5.4
Brownian Eddies and Random Vortex Filaments
.133
5.5
Necessary Conditions for K41
.139
5.6
A Condition Equivalent to K41
.144
References
.148
Mathematical Results Related to the
Navier—
Stokes System
Yakov G. Sinai
.151
1
Introduction
.151
2
Power Series and Diagrams for the Navier-Stokes-System
.154
3
Foias-Temam Theorem for 2.0-Navier-Stokes System with Periodic
Boundary Condition
.158
4
Burgers System and
1-
D Inviscid
Burgers Equation
with Random Forcing
.161
References
.163
List of Participants
.165 |
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| genre | (DE-588)1071861417 Konferenzschrift 2005 Cetraro gnd-content |
| genre_facet | Konferenzschrift 2005 Cetraro |
| id | DE-604.BV023294120 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T20:44:14Z |
| indexdate | 2024-07-09T21:15:10Z |
| institution | BVB |
| isbn | 9783540784920 3540784926 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016478685 |
| oclc_num | 228105435 |
| open_access_boolean | |
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| physical | VIII, 166 S. 235 mm x 155 mm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | SPDE in hydrodynamic: recent progress and prospects lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005 Sergio Albeverio ; Franco Flandoli ; Yakov G. Sinai. Ed.: Giuseppe Da Prato ... Berlin [u.a.] Springer 2008 VIII, 166 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1942 Analyse dimensionnelle - Congrès Fluides, Dynamique des - Modèles mathématiques - Congrès Hydrodynamique - Congrès Hydrodynamique - Modèles mathématiques - Congrès Navier-Stokes, Équations de - Solutions numériques - Congrès Processus stochastiques - Congrès Mathematisches Modell Dimensional analysis Congresses Fluid dynamics Mathematical models Congresses Hydrodynamics Congresses Hydrodynamics Mathematical models Congresses Navier-Stokes equations Numerical solutions Congresses Stochastic processes Congresses Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Hydrodynamik (DE-588)4026302-2 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2005 Cetraro gnd-content Hydrodynamik (DE-588)4026302-2 s Stochastische partielle Differentialgleichung (DE-588)4135969-0 s DE-604 Albeverio, Sergio 1939- Sonstige (DE-588)121093999 oth Flandoli, Franco Sonstige (DE-588)135622360 oth Sinaj, Jakov G. 1935- Sonstige (DE-588)124663079 oth Da Prato, Giuseppe 1936-2023 (DE-588)121352641 edt Lecture notes in mathematics 1942 (DE-604)BV000676446 1942 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016478685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | SPDE in hydrodynamic: recent progress and prospects lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005 Lecture notes in mathematics Analyse dimensionnelle - Congrès Fluides, Dynamique des - Modèles mathématiques - Congrès Hydrodynamique - Congrès Hydrodynamique - Modèles mathématiques - Congrès Navier-Stokes, Équations de - Solutions numériques - Congrès Processus stochastiques - Congrès Mathematisches Modell Dimensional analysis Congresses Fluid dynamics Mathematical models Congresses Hydrodynamics Congresses Hydrodynamics Mathematical models Congresses Navier-Stokes equations Numerical solutions Congresses Stochastic processes Congresses Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd Hydrodynamik (DE-588)4026302-2 gnd |
| subject_GND | (DE-588)4135969-0 (DE-588)4026302-2 (DE-588)1071861417 |
| title | SPDE in hydrodynamic: recent progress and prospects lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005 |
| title_auth | SPDE in hydrodynamic: recent progress and prospects lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005 |
| title_exact_search | SPDE in hydrodynamic: recent progress and prospects lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005 |
| title_exact_search_txtP | SPDE in hydrodynamic: recent progress and prospects lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005 |
| title_full | SPDE in hydrodynamic: recent progress and prospects lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005 Sergio Albeverio ; Franco Flandoli ; Yakov G. Sinai. Ed.: Giuseppe Da Prato ... |
| title_fullStr | SPDE in hydrodynamic: recent progress and prospects lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005 Sergio Albeverio ; Franco Flandoli ; Yakov G. Sinai. Ed.: Giuseppe Da Prato ... |
| title_full_unstemmed | SPDE in hydrodynamic: recent progress and prospects lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005 Sergio Albeverio ; Franco Flandoli ; Yakov G. Sinai. Ed.: Giuseppe Da Prato ... |
| title_short | SPDE in hydrodynamic: recent progress and prospects |
| title_sort | spde in hydrodynamic recent progress and prospects lectures given at the c i m e summer school held in cetraro italy august 29 september 3 2005 |
| title_sub | lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, August 29 - September 3, 2005 |
| topic | Analyse dimensionnelle - Congrès Fluides, Dynamique des - Modèles mathématiques - Congrès Hydrodynamique - Congrès Hydrodynamique - Modèles mathématiques - Congrès Navier-Stokes, Équations de - Solutions numériques - Congrès Processus stochastiques - Congrès Mathematisches Modell Dimensional analysis Congresses Fluid dynamics Mathematical models Congresses Hydrodynamics Congresses Hydrodynamics Mathematical models Congresses Navier-Stokes equations Numerical solutions Congresses Stochastic processes Congresses Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd Hydrodynamik (DE-588)4026302-2 gnd |
| topic_facet | Analyse dimensionnelle - Congrès Fluides, Dynamique des - Modèles mathématiques - Congrès Hydrodynamique - Congrès Hydrodynamique - Modèles mathématiques - Congrès Navier-Stokes, Équations de - Solutions numériques - Congrès Processus stochastiques - Congrès Mathematisches Modell Dimensional analysis Congresses Fluid dynamics Mathematical models Congresses Hydrodynamics Congresses Hydrodynamics Mathematical models Congresses Navier-Stokes equations Numerical solutions Congresses Stochastic processes Congresses Stochastische partielle Differentialgleichung Hydrodynamik Konferenzschrift 2005 Cetraro |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016478685&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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