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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 physici...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [England] ; New York :
Cambridge University Press,
2012.
|
| Colección: | Cambridge tracts in mathematics ;
194. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Kuksin, Sergej B., |d 1955- |e author. |1 https://id.oclc.org/worldcat/entity/E39PBJvRQy7rrXtWBtrpHPbTpP | |
| 245 | 1 | 0 | |a Mathematics of two-dimensional turbulence / |c Sergei Kuksin, Armen Shirikyan. |
| 260 | |a Cambridge [England] ; |a New York : |b Cambridge University Press, |c 2012. | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 490 | 1 | |a Cambridge tracts in mathematics ; |v 194 | |
| 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"-- |c Provided by publisher | ||
| 520 | |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"-- |c Provided by publisher | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 1. Preliminaries -- 2. Two-dimensional Navier-Stokes equations -- 3. Uniqueness of stationary measure and mixing -- 4. Ergodicity and limiting theorems -- 5. Inviscid limit -- 6. Miscellanies -- 7. Appendix -- 8. Solutions to some exercises. | |
| 504 | |a Includes bibliographical references (pages 307-318) and index. | ||
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Hydrodynamics |x Statistical methods. | |
| 650 | 0 | |a Turbulence |x Mathematics. | |
| 650 | 4 | |a Hydrodynamics |x Statistical methods. | |
| 650 | 4 | |a Turbulence |x Mathematics. | |
| 650 | 6 | |a Hydrodynamique |x Méthodes statistiques. | |
| 650 | 6 | |a Turbulence |x Mathématiques. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a SCIENCE |x Mechanics |x Fluids. |2 bisacsh | |
| 650 | 7 | |a Hidrodinámica |2 embne | |
| 650 | 7 | |a Hydrodynamics |x Statistical methods |2 fast | |
| 650 | 7 | |a Turbulence |x Mathematics |2 fast | |
| 700 | 1 | |a Shirikyan, Armen, |e author. | |
| 758 | |i has work: |a Mathematics of two-dimensional turbulence (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGKJ6VFjq9yF36F9K9WyMP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Kuksin, Sergej B., 1955- |t Mathematics of two-dimensional turbulence. |d Cambridge, [England] ; New York : Cambridge University Press, 2012 |z 9781107022829 |w (DLC) 2012024345 |w (OCoLC)793221740 |
| 830 | 0 | |a Cambridge tracts in mathematics ; |v 194. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1025050 |z Texto completo |
| 880 | 8 | |6 505-00/(S |a 4.1.3 Central limit theorem -- 4.2 Random attractors and stationary distributions -- 4.2.1 Random point attractors -- 4.2.2 The Ledrappier-Le Jan-Crauel theorem -- 4.2.3 Ergodic RDS and minimal attractors -- 4.2.4 Application to the Navier-Stokes system -- 4.3 Dependence of stationary measure on the random force -- 4.3.1 Regular dependence on parameters -- 4.3.2 Universality of white-noise perturbations -- 4.4 Relevance of the results for physics -- Notes and comments -- 5 Inviscid limit -- 5.1 Balance relations -- 5.1.1 Energy and enstrophy -- 5.1.2 Balance relations -- 5.1.3 Pointwise exponential estimates -- 5.2 Limiting measures -- 5.2.1 Existence of accumulation points -- 5.2.2 Estimates for the densities of the energy and enstrophy -- 5.2.3 Further properties of the limiting measures -- 5.2.4 Other scalings -- 5.2.5 Kicked Navier-Stokes system -- 5.2.6 Inviscid limit for the complex Ginzburg-Landau equation -- 5.3 Relevance of the results for physics -- Notes and comments -- 6 Miscellanies -- 6.1 3D Navier-Stokes system in thin domains -- 6.1.1 Preliminaries on the Cauchy problem -- 6.1.2 Large-time asymptotics of solutions -- 6.1.3 The limit ε → 0 -- Relevance of the results for physics -- 6.2 Ergodicity and Markov selection -- 6.2.1 Finite-dimensional stochastic differential equations -- 6.2.2 The Da Prato-Debussche-Odasso theorem -- 6.2.3 The Flandoli-Romito theorem -- 6.3 Navier-Stokes equations with very degenerate noise -- 6.3.1 2D Navier-Stokes equations: controllability and mixing properties -- 6.3.2 3D Navier-Stokes equations with degenerate noise -- Appendix -- A.1 Monotone class theorem -- A.2 Standard measurable spaces -- A.3 Projection theorem -- A.4 Gaussian random variables -- A.5 Weak convergence of random measures -- A.6 The Gelfand triple and Yosida approximation -- A.7 Itô formula in Hilbert spaces. | |
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