GLOBAL FLOWS WITH INVARIANT (GIBBS) MEASURES FOR EULER AND NAVIER-STOKES 2-DIMENSIONAL FLUIDS

We construct a family of probability spaces Ωℱ,Pγ), γ<0 associated with the Euler equation for a two dimensional inviscid incompressible fluid which carries a pointwise flow φt (time evolution) leaving Pγ globally invariant. φt is obtained as the limit of Galerkin approximations associated with Euler equations. Pγ is also in invariant measure for a stochastic process associated with a Navier-Stokes equation with viscosity, γ, stochastically perturbed by a white noise force. © 1990 Springer-Verlag.