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Mathematics of two-dimensional turbulence / Sergei Kuksin, Armen Shirikyan

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Cambridge tracts in mathematics ; 194Publisher: Cambridge : Cambridge University Press, 2012Description: 1 Online-Ressource (xvi, 320 pages) : digital, PDF file(s)ISBN:
  • 9781139137119
Subject(s): Additional physical formats: 9781107022829 | 9781107022829. | Erscheint auch als: Mathematics of two-dimensional turbulence. Cambridge [u.a.] : Cambridge Univ. Press, 2012. XVI, 320 S. | Erscheint auch als: 9781107022829 Druck-AusgabeDDC classification:
  • 532.052701519
MSC: MSC: *76-02 | 76F02 | 76D05RVK: RVK: SK 540 | SK 810 | UF 4300 | SK 950LOC classification:
  • QA911
DOI: DOI: 10.1017/CBO9781139137119Online resources: Summary: 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.Summary: Preliminaries -- Two-dimensional Navier-Stokes equations -- Uniqueness of stationary measure and mixing -- Ergodicity and limiting theorems -- Inviscid limit -- MiscellaniesOriginal version: Originalfassung: 2012PPN: PPN: 883361574Package identifier: Produktsigel: ZDB-20-CTM | ZDB-20-CBO
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2012

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