95-290 Esposito R., Marra R., Yau H.T.

Navier-Stokes equations for a stochastic particle systems on the lattice (502K, Postscript) Jun 20, 95

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Abstract. We introduce a class of stochastic models of particles on the cubic lattice $\Bbb Z^d$ with velocities and study the hydrodynamical limit on the diffusive space-time scale. Assuming special initial conditions corresponding to the incompressible regime, we prove that in dimension $d\ge 3$ there is a law of large numbers for the empirical density and the rescaled empirical velocity field. Moreover the limit fields satisfy the corresponding incompressible Navier-Stokes equations,with viscosity matrices characterized by a variational formula, formally equivalent to the Green-Kubo formula.

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