A stochastic infinite dimensional version of the GOY 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) >= 2/3 and zeta(2)=2/3 are given and discussed on the basis of numerical simulations.
Some Rigorous Results on a Stochastic GOY Model
BARSANTI, MICHELE;FLANDOLI, FRANCO
2006-01-01
Abstract
A stochastic infinite dimensional version of the GOY 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) >= 2/3 and zeta(2)=2/3 are given and discussed on the basis of numerical simulations.File in questo prodotto:
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