FM 96-4 Author: Giovanni Gallavotti Title: Equivalence of dynamical ensembles and Navier Stokes equations Abstract: a reversible version of the Navier Stokes equation is studied. A conjecture emerges stating the equivalence between the reversible equation and the usual Navier Stokes equation. The latter appears as a statement of ensembles equivalence in the limit of infinite Reynolds number, which plays the role of the thermodynamic limit. Keywords: Strange attractors, Chaoticity principle, Fluid mechanics, Navier-Stokes equation Fisica, Universita' di Roma La Sapienza, P.le Moro 2, 00185, Roma, Italia. e-mail giovanni@ipparco.roma1.infn.it tel. 6-49914370, fax 6-4957697