Mathematics of two-dimensional turbulence / / Sergei Kuksin, Armen Shirikyan [[electronic resource]]

• Autore: Kuksin Sergej B. <1955->
• Pubblicazione: Cambridge : , : Cambridge University Press, , 2012
• Descrizione fisica: 1 online resource (xvi, 320 pages) : digital, PDF file(s)
• Disciplina: 532/.052701519
• Soggetto topico: Hydrodynamics - Statistical methods; Turbulence - Mathematics
• Persona (resp. second.): ShirikyanArmen
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Preliminaries -- Two-dimensional Navier-Stokes equations -- Uniqueness of stationary measure and mixing -- Ergodicity and limiting theorems -- Inviscid limit -- Miscellanies.
• Sommario/riassunto: 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.
• Titolo autorizzato: Mathematics of two-dimensional turbulence
• ISBN: 1-139-88898-6; 1-139-57957-6; 1-139-56919-8; 1-139-57275-X; 1-139-57352-7; 1-139-57100-1; 1-139-13711-5; 1-283-63871-1; 1-139-57009-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910452678503321
• Lo trovi qui: Univ. Federico II
• Serie: Cambridge tracts in mathematics ; ; 194.