Item Details
Mathematics of TwoDimensional Turbulence
Sergei Kuksin, Armen Shirikyan
 Format
 Book
 Published
 Cambridge, [England] ; New York : Cambridge University Press, c2012.
 Language
 English
 Series
 Cambridge Tracts in Mathematics
 ISBN
 9781107022829 (hardback), 1107022827 (hardback)
 Related Resources
 Cover image
 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"
 "This book deals with basic problems and questions, interesting for physicists and engineers working in the theory of turbulence. Accordingly Chapters 35 (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"
 Contents
 Preliminaries
 Twodimensional NavierStokes equations
 Uniqueness of stationary measure and mixing
 Ergodicity and limiting theorems
 Inviscid limit
 Miscellanies.
 Description
 xvi, 320 p. : ill. ; 24 cm.
 Notes
 Includes bibliographical references (p. 307318) and index.
 Series Statement
 Cambridge tracts in mathematics ; 194
 Technical Details

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LEADER 03036cam a22003978a 4500001 u5843321003 SIRSI005 20121206095909.0008 120613s2012 enka b 001 0 enga 2012024345a 9781107022829 (hardback)a 1107022827 (hardback)a (OCoLC)793221740a DLC b eng c DLC d BTCTA d UKMGB d BDX d OCLCO d YDXCP d OI@ d CDXa pcca QA911 b .K85 2012a 532/.052701519 2 23a MAT029000 2 bisacsha Kuksin, Sergej B., d 1955a Mathematics of twodimensional turbulence / c Sergei Kuksin, Armen Shirikyan.a Cambridge, [England] ; a New York : b Cambridge University Press, c c2012.a xvi, 320 p. : b ill. ; c 24 cm.a Cambridge tracts in mathematics ; v 194a Includes bibliographical references (p. 307318) and index.a "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" c Provided by publisher.a "This book deals with basic problems and questions, interesting for physicists and engineers working in the theory of turbulence. Accordingly Chapters 35 (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.a Preliminaries  Twodimensional NavierStokes equations  Uniqueness of stationary measure and mixing  Ergodicity and limiting theorems  Inviscid limit  Miscellanies.a Hydrodynamics x Statistical methods.a Turbulence x Mathematics.a Shirikyan, Armen.3 Cover image u http://proxy01.its.virginia.edu/login?url=http://assets.cambridge.org/97811070/22829/cover/9781107022829.jpga Cambridge tracts in mathematics ; v 194.a Z0 b VA@a 8a QA911 .K85 2012 w LC i X030850731 k CHECKEDOUT l STACKS m MATH t BOOK
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