Mathematics of two-dimensional turbulence:
"This book deals with basic problems and questions, interesting for physicists and engineers working in the theory of turbulence. Accordingly Chapters 3-5 (which form the main part of this book) end with sections, where we explain the physical relevance of the obtained results. These sections a...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
[2012]
|
| Ausgabe: | First published |
| Schriftenreihe: | Cambridge tracts in mathematics
194 |
| Schlagworte: | |
| Zusammenfassung: | "This book deals with basic problems and questions, interesting for physicists and engineers working in the theory of turbulence. Accordingly Chapters 3-5 (which form the main part of this book) end with sections, where we explain the physical relevance of the obtained results. These sections also provide brief summaries of the corresponding chapters. In Chapters 3 and 4, our main goal is to justify, for the 2D case, the statistical properties of fluid's velocity"-- "This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier-Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) - proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces"-- |
| Beschreibung: | xvi, 320 Seiten Illustrationen 23 cm |
| ISBN: | 9781107022829 1107022827 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematics of two-dimensional turbulence |c Sergei Kuksin, Ecole Polytechnique, Palaiseau ; Armen Shirikyan, Université de Cergy-Pontoise |
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| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c [2012] | |
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| 520 | 3 | |a "This book deals with basic problems and questions, interesting for physicists and engineers working in the theory of turbulence. Accordingly Chapters 3-5 (which form the main part of this book) end with sections, where we explain the physical relevance of the obtained results. These sections also provide brief summaries of the corresponding chapters. In Chapters 3 and 4, our main goal is to justify, for the 2D case, the statistical properties of fluid's velocity"-- | |
| 520 | 3 | |a "This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier-Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) - proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces"-- | |
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Datensatz im Suchindex
| _version_ | 1804184536510103552 |
|---|---|
| adam_txt | |
| any_adam_object | |
| any_adam_object_boolean | |
| author | Kuksin, Sergej B. 1955- Shirikyan, Armen 1970- |
| author_GND | (DE-588)1042649936 (DE-588)1030343624 |
| author_facet | Kuksin, Sergej B. 1955- Shirikyan, Armen 1970- |
| author_role | aut aut |
| author_sort | Kuksin, Sergej B. 1955- |
| author_variant | s b k sb sbk a s as |
| building | Verbundindex |
| bvnumber | BV048537904 |
| classification_rvk | UF 4300 SK 540 SK 810 SK 950 |
| ctrlnum | (OCoLC)815959362 (DE-599)GBV719602580 |
| dewey-full | 532/.052701519 532.0527 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.052701519 532.0527 |
| dewey-search | 532/.052701519 532.0527 |
| dewey-sort | 3532 852701519 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
| edition | First published |
| format | Book |
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| id | DE-604.BV048537904 |
| illustrated | Illustrated |
| index_date | 2024-07-03T20:54:33Z |
| indexdate | 2024-07-10T09:40:54Z |
| institution | BVB |
| isbn | 9781107022829 1107022827 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033914469 |
| oclc_num | 815959362 |
| open_access_boolean | |
| owner | DE-188 |
| owner_facet | DE-188 |
| physical | xvi, 320 Seiten Illustrationen 23 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Kuksin, Sergej B. 1955- Verfasser (DE-588)1042649936 aut Mathematics of two-dimensional turbulence Sergei Kuksin, Ecole Polytechnique, Palaiseau ; Armen Shirikyan, Université de Cergy-Pontoise First published Cambridge [u.a.] Cambridge Univ. Press [2012] xvi, 320 Seiten Illustrationen 23 cm txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 194 "This book deals with basic problems and questions, interesting for physicists and engineers working in the theory of turbulence. Accordingly Chapters 3-5 (which form the main part of this book) end with sections, where we explain the physical relevance of the obtained results. These sections also provide brief summaries of the corresponding chapters. In Chapters 3 and 4, our main goal is to justify, for the 2D case, the statistical properties of fluid's velocity"-- "This book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier-Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) - proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces"-- Turbulenztheorie (DE-588)4186472-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Turbulence Mathematics Hydrodynamics / Statistical methods Turbulence / Mathematics Hydrodynamik (DE-588)4026302-2 s Statistik (DE-588)4056995-0 s Turbulenztheorie (DE-588)4186472-4 s DE-604 Navier-Stokes-Gleichung (DE-588)4041456-5 s Shirikyan, Armen 1970- Verfasser (DE-588)1030343624 aut Erscheint auch als Online-Ausgabe 978-1-139-13711-9 Cambridge tracts in mathematics 194 (DE-604)BV000000001 194 |
| spellingShingle | Kuksin, Sergej B. 1955- Shirikyan, Armen 1970- Mathematics of two-dimensional turbulence Cambridge tracts in mathematics Turbulenztheorie (DE-588)4186472-4 gnd Statistik (DE-588)4056995-0 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Hydrodynamik (DE-588)4026302-2 gnd |
| subject_GND | (DE-588)4186472-4 (DE-588)4056995-0 (DE-588)4041456-5 (DE-588)4026302-2 |
| title | Mathematics of two-dimensional turbulence |
| title_auth | Mathematics of two-dimensional turbulence |
| title_exact_search | Mathematics of two-dimensional turbulence |
| title_exact_search_txtP | Mathematics of two-dimensional turbulence |
| title_full | Mathematics of two-dimensional turbulence Sergei Kuksin, Ecole Polytechnique, Palaiseau ; Armen Shirikyan, Université de Cergy-Pontoise |
| title_fullStr | Mathematics of two-dimensional turbulence Sergei Kuksin, Ecole Polytechnique, Palaiseau ; Armen Shirikyan, Université de Cergy-Pontoise |
| title_full_unstemmed | Mathematics of two-dimensional turbulence Sergei Kuksin, Ecole Polytechnique, Palaiseau ; Armen Shirikyan, Université de Cergy-Pontoise |
| title_short | Mathematics of two-dimensional turbulence |
| title_sort | mathematics of two dimensional turbulence |
| topic | Turbulenztheorie (DE-588)4186472-4 gnd Statistik (DE-588)4056995-0 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Hydrodynamik (DE-588)4026302-2 gnd |
| topic_facet | Turbulenztheorie Statistik Navier-Stokes-Gleichung Hydrodynamik |
| volume_link | (DE-604)BV000000001 |
| work_keys_str_mv | AT kuksinsergejb mathematicsoftwodimensionalturbulence AT shirikyanarmen mathematicsoftwodimensionalturbulence |