Sufficient conditions for flux scaling laws in the stochastic Navier-Stokes equations

We derive a sufficient condition under which a version of Kolmogorov's 4/5 law can be rigorously proved for stationary solutions of the 3D stochastic Navier-Stokes equations. We name this condition 'weak anomalous dissipation condition'. A similar condition allows to prove flux scaling laws for the 2D stochastic Navier-Stokes equations, including a scaling law for the inverse cascade. We also derive necessary conditions which are needed for the same scaling laws to hold.

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