Mathematics of two-dimensional turbulence:
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 ass...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2012
|
| Series: | Cambridge tracts in mathematics
194 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | 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 |
| Physical Description: | 1 Online-Ressource (xvi, 320 Seiten) |
| ISBN: | 9781139137119 |
| DOI: | 10.1017/CBO9781139137119 |
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| 505 | 8 | |a Preliminaries -- Two-dimensional Navier-Stokes equations -- Uniqueness of stationary measure and mixing -- Ergodicity and limiting theorems -- Inviscid limit -- Miscellanies | |
| 520 | |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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Record in the Search Index
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| author | Kuksin, Sergej B. 1955- |
| author_GND | (DE-588)1042649936 (DE-588)1030343624 |
| author_facet | Kuksin, Sergej B. 1955- |
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| building | Verbundindex |
| bvnumber | BV043941788 |
| classification_rvk | SK 540 SK 810 SK 950 UF 4300 |
| collection | ZDB-20-CBO |
| contents | Preliminaries -- Two-dimensional Navier-Stokes equations -- Uniqueness of stationary measure and mixing -- Ergodicity and limiting theorems -- Inviscid limit -- Miscellanies |
| ctrlnum | (ZDB-20-CBO)CR9781139137119 (OCoLC)847029230 (DE-599)BVBBV043941788 |
| dewey-full | 532/.052701519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
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| discipline | Physik Mathematik |
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| id | DE-604.BV043941788 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781139137119 |
| language | English |
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| physical | 1 Online-Ressource (xvi, 320 Seiten) |
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| publishDate | 2012 |
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| spelling | Kuksin, Sergej B. 1955- Verfasser (DE-588)1042649936 aut Mathematics of two-dimensional turbulence Sergei Kuksin, Armen Shirikyan Cambridge Cambridge University Press 2012 1 Online-Ressource (xvi, 320 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 194 Preliminaries -- Two-dimensional Navier-Stokes equations -- Uniqueness of stationary measure and mixing -- Ergodicity and limiting theorems -- Inviscid limit -- Miscellanies 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 Mathematik Hydrodynamics / Statistical methods Turbulence / Mathematics Turbulenztheorie (DE-588)4186472-4 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Hydrodynamik (DE-588)4026302-2 gnd rswk-swf 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- Sonstige (DE-588)1030343624 oth Erscheint auch als Druck-Ausgabe 978-1-107-02282-9 https://doi.org/10.1017/CBO9781139137119 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kuksin, Sergej B. 1955- Mathematics of two-dimensional turbulence Preliminaries -- Two-dimensional Navier-Stokes equations -- Uniqueness of stationary measure and mixing -- Ergodicity and limiting theorems -- Inviscid limit -- Miscellanies Mathematik Hydrodynamics / Statistical methods Turbulence / Mathematics Turbulenztheorie (DE-588)4186472-4 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Statistik (DE-588)4056995-0 gnd Hydrodynamik (DE-588)4026302-2 gnd |
| subject_GND | (DE-588)4186472-4 (DE-588)4041456-5 (DE-588)4056995-0 (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_full | Mathematics of two-dimensional turbulence Sergei Kuksin, Armen Shirikyan |
| title_fullStr | Mathematics of two-dimensional turbulence Sergei Kuksin, Armen Shirikyan |
| title_full_unstemmed | Mathematics of two-dimensional turbulence Sergei Kuksin, Armen Shirikyan |
| title_short | Mathematics of two-dimensional turbulence |
| title_sort | mathematics of two dimensional turbulence |
| topic | Mathematik Hydrodynamics / Statistical methods Turbulence / Mathematics Turbulenztheorie (DE-588)4186472-4 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Statistik (DE-588)4056995-0 gnd Hydrodynamik (DE-588)4026302-2 gnd |
| topic_facet | Mathematik Hydrodynamics / Statistical methods Turbulence / Mathematics Turbulenztheorie Navier-Stokes-Gleichung Statistik Hydrodynamik |
| url | https://doi.org/10.1017/CBO9781139137119 |
| work_keys_str_mv | AT kuksinsergejb mathematicsoftwodimensionalturbulence AT shirikyanarmen mathematicsoftwodimensionalturbulence |