 95290 Esposito R., Marra R., Yau H.T.
 NavierStokes equations for a stochastic
particle systems on the lattice
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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 spacetime 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 NavierStokes
equations,with viscosity matrices characterized by a variational
formula, formally equivalent to the GreenKubo formula.
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