Mathematics of twodimensional turbulence
 Responsibility
 Sergei Kuksin, Armen Shirikyan.
 Imprint
 Cambridge, [England] ; New York : Cambridge University Press, 2012.
 Physical description
 xvi, 320 p. : ill. ; 24 cm.
 Series
 Cambridge tracts in mathematics ; 194.
Access
Available online
Science Library (Li and Ma)
Stacks
Call number  Status 

QA911 .K85 2012  Unknown 
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Creators/Contributors
 Author/Creator
 Kuksin, Sergej B., 1955
 Contributor
 Shirikyan, Armen.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 307318) and index.
 Contents

 1. Preliminaries 2. Twodimensional NavierStokes 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.
 (source: Nielsen Book Data)9781107022829 20160610
 Publisher's Summary
 This book is dedicated to the mathematical study of twodimensional statistical hydrodynamics and turbulence, described by the 2D NavierStokes 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.
(source: Nielsen Book Data)9781107022829 20160610  Supplemental links
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Bibliographic information
 Publication date
 2012
 Series
 Cambridge tracts in mathematics ; 194
 ISBN
 9781107022829 (hardback)
 1107022827 (hardback)