INVARIANT MEASURES OF LÉVY-KHINCHINE TYPE FOR 2D FLUIDS

A survey of results on invariant measures of the Lévy-Khinchine type for 2D Euler and stochastic Navier–Stokes equations is given. Uniqueness results of the corresponding Liouville respectively Kolmogorov flows are discussed. Stochastic dynamics associated with the invariant measures are also discussed (stochastic Stokes equation for the vorticity in the Gaussian case, Doob's independent Brownian motions process in the compound Poisson case).