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Type: Artigo
Title: A note on statistical solutions of the three-dimensional Navier–Stokes equations: The stationary case
Author(s)/Inventor(s): Foias, Ciprian
Rosa, Ricardo Martins da Silva
Temam, Roger
Abstract: Indisponível.
Abstract: Stationary statistical solutions of the three-dimensional Navier–Stokes equations for incompressible fluids are considered. They are a mathematical formalization of the notion of ensemble average for turbulent flows in statistical equilibrium in time. They are also a generalization of the notion of invariant measure to the case of the three-dimensional Navier–Stokes equations, for which a global uniqueness result is not known to exist and a semigroup may not be well-defined in the classical sense. The two classical definitions of stationary statistical solutions are considered and compared, one of them being a particular case of the other and possessing a number of useful properties. Furthermore, the so-called time-average stationary statistical solutions, obtained as generalized limits of time averages of weak solutions as the averaging time goes to infinity are shown to belong to this more restrictive class. A recurrent type result is also obtained for statistical solutions satisfying an accretion condition. Finally, the weak global attractor of the three-dimensional Navier–Stokes equations is considered, and in particular it is shown that there exists a topologically large subset of the weak global attractor which is of full measure with respect to that particular class of stationary statistical solutions and which has a certain regularity property.
Keywords: Navier–Stokes equations
Vishik–Fursikov stationary statistical
Production unit: Núcleo Interdisciplinar de Dinâmica dos Fluidos
Publisher: Elsevier
In: Comptes Rendus Mathématique
Volume: 348
Issue: 5-6
Issue Date: 24-Feb-2010
DOI: 10.1016/j.crma.2009.12.018
Publisher country: Brasil
Language: eng
Right access: Acesso Aberto
ISSN: 1631-073X
Appears in Collections:Engenharias

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