ON THE DERIVATION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATION FOR HAMILTONIAN PARTICLE-SYSTEMS

We consider a Hamiltonian particle system interacting by means of a pair potential. We look at the behavior of the system on a space scale of order epsilon-1, times of order epsilon-2 and mean velocities of order epsilon, with epsilon a scale parameter. Assuming that the phase space density of the particles is given by a series in epsilon (the analog of the Chapman-Enskog expansion), the behavior of the system under this rescaling is described, to the lowest order in epsilon, by the incompressible Navier-Stokes equations. The viscosity is given in terms of microscopic correlations, and its expression agrees with the Green-Kubo formula.