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 ζp of the structure function are investigated. Necessary and sufficient conditions for ζ2≥ 2/3 and ζ2=2/3 are given and discussed on the basis of numerical simulations.
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Barbato, D., Barsanti, M., Bessaih, H. et al. Some Rigorous Results on a Stochastic GOY Model. J Stat Phys 125, 677–716 (2006). https://doi.org/10.1007/s10955-006-9203-y
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DOI: https://doi.org/10.1007/s10955-006-9203-y