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The Kolmogorov equation associated to a stochastic 2D Euler equations withtransport type noise and random initial conditions is studied by a directapproach, based on Fourier analysis, Galerkin approximation and Wiener chaosmethods. The method allows us to generalize previous results and to understandthe role of the regularity of the noise, in relation to a limiting value ofroughness.

Kolmogorov equations associated to the stochastic 2D Euler equations