# Mathematics of Two-Dimensional 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 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"--
"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"--
Contents
• Preliminaries
• Two-dimensional Navier-Stokes 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. 307-318) and index.
Series Statement
Cambridge tracts in mathematics ; 194
Technical Details
• Access in Virgo Classic
• Staff View

LEADER 03036cam a22003978a 4500
001 u5843321
003 SIRSI
005 20121206095909.0
008 120613s2012 enka b 001 0 eng
a| 2012024345
a| 9781107022829 (hardback)
a| 1107022827 (hardback)
a| (OCoLC)793221740
a| DLC b| eng c| DLC d| BTCTA d| UKMGB d| BDX d| OCLCO d| YDXCP d| OI@ d| CDX
a| pcc
050
0
0
a| QA911 b| .K85 2012
082
0
0
a| 532/.052701519 2| 23
a| MAT029000 2| bisacsh
100
1

a| Kuksin, Sergej B., d| 1955-
245
1
0
a| Mathematics of two-dimensional 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.
490
1

a| Cambridge tracts in mathematics ; v| 194
a| Includes bibliographical references (p. 307-318) and index.
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.
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.
505
0

a| Preliminaries -- Two-dimensional Navier-Stokes equations -- Uniqueness of stationary measure and mixing -- Ergodicity and limiting theorems -- Inviscid limit -- Miscellanies.
650

0
a| Hydrodynamics x| Statistical methods.
650

0
a| Turbulence x| Mathematics.
700
1

a| Shirikyan, Armen.
856
4
2
3| Cover image u| http://proxy01.its.virginia.edu/login?url=http://assets.cambridge.org/97811070/22829/cover/9781107022829.jpg
830

0
a| Cambridge tracts in mathematics ; v| 194.
a| Z0 b| VA@
a| 8
a| QA911 .K85 2012 w| LC i| X030850731 k| CHECKEDOUT l| STACKS m| MATH t| BOOK
▾See more
▴See less