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Incompressible fluid equations are studied with UV cut-off and in periodicboundary conditions. Properties of the resulting ODEs holding uniformly in thecut-off are considered and, in particular, are conjectured to be equivalent toproperties of other time reversible equations. Reversible equations with thesame regularization and describing equivalently the fluid, and the fluctuationsof large classes of observables, are examined in the context of the "ChaoticHypothesis", "Axiom C" and the "Fluctuation Theorem".

Viscosity, Reversibillity, Chaotic Hypothesis, Fluctuation Theorem and Lyapunov Pairing