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BestsellerE-book
Author Kuksin, Sergej B., 1955- author.

Title Mathematics of two-dimensional turbulence / Sergei Kuksin, Armen Shirikyan.

Publication Info. Cambridge [England] ; New York : Cambridge University Press, 2012.

Item Status

Description 1 online resource.
data file
Physical Medium polychrome
Series Cambridge tracts in mathematics ; 194
Cambridge tracts in mathematics ; 194.
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"-- Provided by publisher.
"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"-- Provided by publisher.
Contents 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.
Bibliography Includes bibliographical references (pages 307-318) and index.
Local Note eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject Hydrodynamics -- Statistical methods.
Hydrodynamics -- Statistical methods.
Hydrodynamics.
Turbulence -- Mathematics.
Turbulence -- Mathematics.
Turbulence.
Genre/Form Electronic books.
Electronic book.
Electronic books.
Added Author Shirikyan, Armen., author.
Other Form: Print version: Kuksin, Sergej B., 1955- Mathematics of two-dimensional turbulence. Cambridge, [England] ; New York : Cambridge University Press, 2012 9781107022829 (DLC) 2012024345 (OCoLC)793221740
ISBN 9781139569194 (electronic book)
1139569198 (electronic book)
9781139137119 (electronic book)
1139137115 (electronic book)
9781139571005
1139571001
9781139572750 (ebook)
113957275X
9781139572750
9781107022829
1107022827
661395117X
9786613951175
1283638711
9781283638715
Standard No. 9786613951175