Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids

We construct a family of probability spaces,P ), <0 associated with the Euler equation for a two dimensional inviscid incompressible fluid which carries a pointwise flow _t (time evolution) leavingP globally invariant. _t is obtained as the limit of Galerkin approximations associated with Euler equations.P is also in invariant measure for a stochastic process associated with a Navier-Stokes equation with viscosity, , stochastically perturbed by a white noise force. Dedication. After completion of this work the terrible news of the sudden death of Raphael Høgh-Krohn reached us. In deep sorrow we mourn his departure. The present work has its roots in previous inspiring work by him and we dedicate it to him as a small sign of our gratitude.