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Some rigorous results on a stochastic GOY model. (English) Zbl 1107.82057
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.

82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76F05 Isotropic turbulence; homogeneous turbulence
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