  After a short review of recent progresses in 2D Euler equations with random
initial conditions and noise, some of the recent results are improved by
exploiting a priori estimates on the associated infinite dimensional
Fokker-Planck equation. The regularity class of solutions investigated here
does not allow energy- or enstrophy-type estimates, but only bounds in
probability with respect to suitable distributions of the initial conditions.
This is a remarkable application of Fokker-Planck equations in infinite
dimensions. Among the example of random initial conditions we consider Gibbsian
measures based on renormalized kinetic energy.
