On the derivation of new non-classical hydrodynamic equations for Hamiltonian particle systems

Abstract

We consider a Hamiltonian system of particles, interacting through of a smooth pair potential. We look at 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, under initial conditions where the system is in a local Gibbs state with parameters corresponding to density and temperature with gradients of order 1. Assuming that the phase space density of the particles is given by a suitable series in {\epsilon} the behavior of the system under this rescaling is described, to the lowest order in {\epsilon}, by new non-classical hydrodynamic equations that cannot be derived from the compressible Navier-Stokes equations in the small Mac number limit. The analogous equations in kinetic theory are called ghost effect equations.