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Solution d’un problème sur les itérés d’un opérateur positif sur C ( K ) et propriétés de moyennes associées

Gustave ChoquetCiprian Foias — 1975

Annales de l'institut Fourier

Soit T un opérateur linéaire positif sur 𝒞 ( K ) (où K est un compact). On montre que si inf. { T 1 n ; n > 0 } < 1 , la suite des ( T n ) converge uniformément vers 0, et que si sup. { T 1 n ; n > 0 } > 1 la suite des ( T n ) converge uniformément vers + . Puis on applique ces deux énoncés à l’étude des suites : 0 n - 1 T i f / n et ( T n f ) 1 / n  ; on donne en particulier plusieurs critères de convergence uniforme de ces suites.

Limiting Behavior for an Iterated Viscosity

Ciprian FoiasMichael S. JollyOscar P. Manley — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

The behavior of an ordinary differential equation for the low wave number velocity mode is analyzed. This equation was derived in [5] by an iterative process on the two-dimensional Navier-Stokes equations (NSE). It resembles the NSE in form, except that the kinematic viscosity is replaced by an iterated viscosity which is a partial sum, dependent on the low-mode velocity. The convergence of this sum as the number of iterations is taken to be arbitrarily large is explored. This leads to a limiting...

Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations

Ciprian FoiasRicardo M. S. RosaRoger Temam — 2013

Annales de l’institut Fourier

This work is devoted to the concept of statistical solution of the Navier-Stokes equations, proposed as a rigorous mathematical object to address the fundamental concept of ensemble average used in the study of the conventional theory of fully developed turbulence. Two types of statistical solutions have been proposed in the 1970’s, one by Foias and Prodi and the other one by Vishik and Fursikov. In this article, a new, intermediate type of statistical solution is introduced and studied. This solution...

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