THE RATE OF CONVERGENCE OF APPROXIMATIONS FOR THE CLOSURE OF THE FRIEDMAN-KELLER CHAIN IN THE CASE OF LARGE REYNOLDS-NUMBERS

The infinite chain of Friedman-Keller equations is studied that descri bes the evolution of the entire set of moments of a statistical soluti on of an abstract analogue of the Navier-Stokes system. The problem of closure of this chain is investigated. This problem consists in const ructing a sequence of problems U-N = 0 of N unknown functions whose so lutions M(N) = (M(1)(N),...,M(N)(N), 0, 0,...) approximate the system of moments M = (M(1),...,M(k),...) as N --> +infinity. The case of lar ge Reynolds numbers is considered. Exponential rate of convergence of M(N) to M as N --> infinity is proved.