- 95-290 Esposito R., Marra R., Yau H.T.
- Navier-Stokes equations for a stochastic
particle systems on the lattice
Jun 20, 95
(auto. generated ps),
of related papers
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.