Authors : Giovanni Gallavotti

Title:: Navier-Stokes Equations and equivalence conjectures/\

Abstract: General considerations on the Equivalence conjectures and a review of few mathematical results. The conjectures deal with properties of the NS equations regularized at ultraviolet (UV) cut off $|\kk|0$ has been shown to imply uniform UV-independent bounds on all derivatives of $\bf u$, leading to think that positivity of $\alpha$ only allows for large-$N$ deviations to negative values as $N\to\infty$. (4) For the non-local observables, defined by the spectrum of the Jacobian of the evolutions, approximate equivalence has been reported in a sense discussed here as well as a surprising, approximate, ``pairing rule'' for the Lyapunov exponents.

Keywords: ensembles equivalence, reversible viscosity, irreversibility

Giovanni Gallavotti
INFN-Roma1 and Universit\`a "La Sapienza” Roma, Italy