an:05126764
Zbl 1107.82057
Barbato, D.; Barsanti, M.; Bessaih, H.; Flandoli, F.
Some rigorous results on a stochastic GOY model
EN
J. Stat. Phys. 125, No. 3, 673-712 (2006).
00191925
2006
j
82C41 76D05 76F05
stochastic GOY model; invariant measures; structure function; asymptotic exponents
Summary: A stochastic infinite dimensional version of the Gledzer-Ohkitani-Ymada model is rigorously investigated. Well posedness of strong solutions, existence and \(p\)-integrability of invariant measures is proved. Existence of solutions to the zero viscosity equation is also proved. With these preliminary results, the asymptotic exponents \(\zeta_p\) of the structure function are investigated. Necessary and sufficient conditions for \(\zeta_2 \geq 2/3\) and \(\zeta_2 = 2/3\) are given and discussed on the basis of numerical simulations.