ONE-DIMENSIONAL HARD-ROD CARICATURE OF HYDRODYNAMICS - NAVIER-STOKES CORRECTION FOR LOCAL EQUILIBRIUM INITIAL STATES

A one-dimensional system, consisting of identical hard-rod particles o f length a is studied in the hydrodynamical limit. A ''Navier-Stokes c orrection'' to the Euler equation is found for an initial local equili brium family of states P-c,epsilon > 0, of constant density, The corre ction is given, at t similar to 0, by a non-linear second order differ ential operator acting on f(q,v), the hydrodynamical density at a poin t q is an element of R-1 of the ''species'' of fluid with velocity v i s an element of R-1.