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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aMathematics of two-dimensional turbulence /$fSergei Kuksin, Armen Shirikyan$b[electronic resource]
210  1$aCambridge :$cCambridge University Press,$d2012.
215   $a1 online resource (xvi, 320 pages) $cdigital, PDF file(s)
225 1 $aCambridge tracts in mathematics ;$v194
300   $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
311   $a1-107-02282-7 
320   $aIncludes bibliographical references and index.
327   $aPreliminaries -- Two-dimensional Navier-Stokes equations -- Uniqueness of stationary measure and mixing -- Ergodicity and limiting theorems -- Inviscid limit -- Miscellanies.
330   $aThis book is dedicated to the mathematical study of two-dimensional statistical hydrodynamics and turbulence, described by the 2D Navier-Stokes system with a random force. The authors' main goal is to justify the statistical properties of a fluid's velocity field u(t,x) that physicists assume in their work. They rigorously prove that u(t,x) converges, as time grows, to a statistical equilibrium, independent of initial data. They use this to study ergodic properties of u(t,x) - proving, in particular, that observables f(u(t,.)) satisfy the strong law of large numbers and central limit theorem. They also discuss the inviscid limit when viscosity goes to zero, normalising the force so that the energy of solutions stays constant, while their Reynolds numbers grow to infinity. They show that then the statistical equilibria converge to invariant measures of the 2D Euler equation and study these measures. The methods apply to other nonlinear PDEs perturbed by random forces.
410  0$aCambridge tracts in mathematics ;$v194.
606   $aHydrodynamics$xStatistical methods
606   $aTurbulence$xMathematics
615  0$aHydrodynamics$xStatistical methods.
615  0$aTurbulence$xMathematics.
676   $a532/.052701519
700   $aKuksin$b Sergej B.$f1955-$060265
702   $aShirikyan$b Armen
801  0$bUkCbUP
801  1$bUkCbUP
906   $aBOOK
912   $a9910452678503321
996   $aMathematics of two-dimensional turbulence$92474539
997   $aUNINA