LEADER 04659nam 22006852 450 001 9910450054503321 005 20160428174355.0 010 $a1-107-11154-4 010 $a1-280-41654-8 010 $a9786610416547 010 $a0-511-17438-1 010 $a0-511-03936-0 010 $a0-511-15422-4 010 $a0-511-32829-X 010 $a0-511-54675-0 010 $a0-511-05242-1 035 $a(CKB)1000000000005482 035 $a(EBL)201945 035 $a(OCoLC)56416088 035 $a(SSID)ssj0000208926 035 $a(PQKBManifestationID)11190537 035 $a(PQKBTitleCode)TC0000208926 035 $a(PQKBWorkID)10245446 035 $a(PQKB)11556719 035 $a(UkCbUP)CR9780511546754 035 $a(MiAaPQ)EBC201945 035 $a(Au-PeEL)EBL201945 035 $a(CaPaEBR)ebr10006796 035 $a(CaONFJC)MIL41654 035 $a(EXLCZ)991000000000005482 100 $a20090508d2001|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNavier-Stokes equations and turbulence /$fC. Foias [and three others]$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2001. 215 $a1 online resource (xiv, 347 pages) $cdigital, PDF file(s) 225 1 $aEncyclopedia of mathematics and its applications ;$vvolume 83 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-06460-0 311 $a0-521-36032-3 320 $aIncludes bibliographical references (p. 331-342) and index. 327 $tIntroduction and Overview of Turbulence --$tViscous Fluids. The Navier-Stokes Equations --$tTurbulence: Where the Interests of Engineers and Mathematicians Overlap --$tElements of the Theories of Turbulence of Kolmogorov and Kraichnan --$tFunction Spaces, Functional Inequalities, and Dimensional Analysis --$tElements of the Mathematical Theory of the Navier-Stokes Equations --$tEnergy and Enstrophy --$tBoundary Value Problems --$tHelmholtz-Leray Decomposition of Vector Fields --$tWeak Formulation of the Navier-Stokes Equations --$tFunction Spaces --$tThe Stokes Operator --$tExistence and Uniqueness of Solutions: The Main Results --$tAnalyticity in Time --$tGevrey Class Regularity and the Decay of the Fourier Coefficients --$tFunction Spaces for the Whole-Space Case --$tThe No-Slip Case with Moving Boundaries --$tDissipation Rate of Flows --$tNondimensional Estimates and the Grashof Number --$tMathematical Complements --$tProofs of Technical Results in Chapter II --$tFinite Dimensionality of Flows --$tDetermining Modes --$tDetermining Nodes --$tAttractors and Their Fractal Dimension --$tApproximate Inertial Manifolds --$tProofs of Technical Results in Chapter III --$tStationary Statistical Solutions of the Navier-Stokes Equations, Time Averages, and Attractors --$tMathematical Framework, Definition of Stationary Statistical Solutions, and Banach Generalized Limits --$tInvariant Measures and Stationary Statistical Solutions in Dimension 2 --$tStationary Statistical Solutions in Dimension 3 --$tAttractors and Stationary Statistical Solutions. 330 $aThis book aims to bridge the gap between practising mathematicians and the practitioners of turbulence theory. It presents the mathematical theory of turbulence to engineers and physicists, and the physical theory of turbulence to mathematicians. The book is the result of many years of research by the authors to analyse turbulence using Sobolev spaces and functional analysis. In this way the authors have recovered parts of the conventional theory of turbulence, deriving rigorously from the Navier-Stokes equations what had been arrived at earlier by phenomenological arguments. The mathematical technicalities are kept to a minimum within the book, enabling the language to be at a level understood by a broad audience. Each chapter is accompanied by appendices giving full details of the mathematical proofs and subtleties. This unique presentation should ensure a volume of interest to mathematicians, engineers and physicists. 410 0$aEncyclopedia of mathematics and its applications ;$vv. 83. 517 3 $aNavier-Stokes Equations & Turbulence 606 $aTurbulence 606 $aNavier-Stokes equations 615 0$aTurbulence. 615 0$aNavier-Stokes equations. 676 $a532/.0527 700 $aFoias?$b Ciprian$021981 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910450054503321 996 $aNavier-Stokes equations and turbulence$92482471 997 $aUNINA