One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States

Abstract:

A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states , of constant density. The correction is given, at , by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point of the “species” of fluid with velocity .