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Mathematics of two-dimensional turbu...

Kuksin, Sergej B., (1955-)

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Mathematics of two-dimensional turbulence /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Mathematics of two-dimensional turbulence // Sergei Kuksin, Armen Shirikyan.
作者:	Kuksin, Sergej B.,
其他作者:	Shirikyan, Armen.
出版者:	Cambridge, [England] ;Cambridge University Press, : 2012.,
面頁冊數:	xvi, 320 p. :ill. ;25 cm.
標題:	Hydrodynamics - Statistical methods. -
ISBN:	9781107022829 (hbk.) :

Mathematics of two-dimensional turbulence /
Kuksin, Sergej B.,1955-

Mathematics of two-dimensional turbulence /Sergei Kuksin, Armen Shirikyan. - Cambridge, [England] ;Cambridge University Press,2012. - xvi, 320 p. :ill. ;25 cm. - Cambridge tracts in mathematics ;194.

Includes bibliographical references (p. 307-318) and index.

Preliminaries --

"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"--

ISBN: 9781107022829 (hbk.) :US85.00

LCCN: 2012024345Subjects--Topical Terms:

2012738
Hydrodynamics
--Statistical methods.

LC Class. No.: QA911 / .K85 2012

Dewey Class. No.: 532/.052701519

Mathematics of two-dimensional turbulence /
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100 1 $a Kuksin, Sergej B., $d 1955- $3 705217
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 xvi, 320 p. : $b ill. ; $c 25 cm.
490 1 0 $a Cambridge tracts in mathematics ; $v 194
504 $a Includes bibliographical references (p. 307-318) and index.
505 0 # $t Preliminaries -- $t Two-dimensional Navier-Stokes equations -- $t Uniqueness of stationary measure and mixing -- $t Ergodicity and limiting theorems -- $t Inviscid limit -- $t Miscellanies -- $t Appendix -- $t Solutions to some exercises.
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.
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.
650 # 0 $a Hydrodynamics $x Statistical methods. $3 2012738
650 # 0 $a Turbulence $x Mathematics. $3 896846
700 1 # $a Shirikyan, Armen. $3 2012737