THE DESCRIPTION OF MANY-PARTICLE SYSTEMS BY THE EQUATIONS FOR A VISCOUS, COMPRESSIBLE, BAROTROPIC FLUID

We consider many-particle systems with a Hamiltonian dynamics supplemented by a friction term. Both the interaction potential and the additional friction force are supposed to be long range in comparison with the typical distance between neighboring particles. It is shown that in a zero-temperature situation the empirical processes of the positions and the velocities converge to solutions of the continuity equation and the compressible, barotropic Navier-Stokes equation, respectively, in the limit as the particle number tends to infinity.