Kolmogorov equations associated to the stochastic two dimensional euler equations

The Kolmogorov equation associated to a stochastic two dimensional Euler equation with transport type noise and random initial conditions is studied in the weak sense by a direct approach, based on Fourier analysis, Galerkin approximation, and Wiener chaos methods. The method allows us to generalize previous results and to understand the role of the regularity of the noise, in relation to a limiting value of roughness.