A. V. Fursikov, O. Yu. Imanuvilov, “The rate of convergence of approximations for the closure of the Friedman–Keller chain in the case of large Reynolds numbers”, Mat. Sb., 1994, Volume 185, Number 2,Pages <nobr>115

This article is cited in 6 papers

The rate of convergence of approximations for the closure of the Friedman–Keller chain in the case of large Reynolds numbers

A. V. Fursikov^a, O. Yu. Imanuvilov^b

^a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Moscow State Forest University

Abstract: The infinite chain of Friedman–Keller equations is studied that describes the evolution of the entire set of moments of a statistical solution of an abstract analogue of the Navier–Stokes system. The problem of closure of this chain is investigated. This problem consists in constructing a sequence of problems $\mathfrak{A}_N=0$ of $N$ unknown functions whose solutions $M^N=(M_1^N,\dots,M_N^N,0,0,\dots)$ approximate the system of moments $M=(M_1,\dots,M_k,\dots)$ as $N\to+\infty$. The case of large Reynolds numbers is considered. Exponential rate of convergence of $~M^N$ to $M$ as $N\to\infty$ is proved.

UDC: 517.958

MSC: 35A45, 35Q30, 35Q53, 58D25

Received: 24.03.1993