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Mathematics of two-dimensional turbu...

Kuksin, Sergej B., (1955-)

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Mathematics of two-dimensional turbulence

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematics of two-dimensional turbulence/ Sergei Kuksin, Armen Shirikyan.
Author:	Kuksin, Sergej B.,
other author:	Shirikyan, Armen.
Published:	Cambridge :Cambridge University Press, : 2012.,
Description:	xvi, 320 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	Preliminaries -- Two-dimensional Navier-Stokes equations -- Uniqueness of stationary measure and mixing -- Ergodicity and limiting theorems -- Inviscid limit -- Miscellanies.
Subject:	Hydrodynamics - Statistical methods. -
Online resource:	https://doi.org/10.1017/CBO9781139137119
ISBN:	9781139137119

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

Mathematics of two-dimensional turbulence[electronic resource] /Sergei Kuksin, Armen Shirikyan. - Cambridge :Cambridge University Press,2012. - xvi, 320 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;194. - Cambridge tracts in mathematics ;194..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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

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.

ISBN: 9781139137119Subjects--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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245 1 0 $a Mathematics of two-dimensional turbulence $h [electronic resource] / $c Sergei Kuksin, Armen Shirikyan.
260 $a Cambridge : $b Cambridge University Press, $c 2012.
300 $a xvi, 320 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 194
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a Preliminaries -- Two-dimensional Navier-Stokes equations -- Uniqueness of stationary measure and mixing -- Ergodicity and limiting theorems -- Inviscid limit -- Miscellanies.
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.
650 0 $a Hydrodynamics $x Statistical methods. $3 2012738
650 0 $a Turbulence $x Mathematics. $3 896846
700 1 $a Shirikyan, Armen. $3 2012737
830 0 $a Cambridge tracts in mathematics ; $v 194. $3 3470478
856 4 0 $u https://doi.org/10.1017/CBO9781139137119