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After a short review of recent progresses in 2D Euler equations with randominitial conditions and noise, some of the recent results are improved byexploiting a priori estimates on the associated infinite dimensionalFokker-Planck equation. The regularity class of solutions investigated heredoes not allow energy- or enstrophy-type estimates, but only bounds inprobability with respect to suitable distributions of the initial conditions.This is a remarkable application of Fokker-Planck equations in infinitedimensions. Among the example of random initial conditions we consider Gibbsianmeasures based on renormalized kinetic energy.

Fokker-Planck equation for dissipative 2D Euler equations with cylindrical noise