On the Hydrodynamic Limit of the Enskog Equation

Abstract

The Enskog equation in the hydrodynamie limit is investigated. If the Knudsen number $\epsilon$ and the scale of diameter $a$ of the hard sphere particles are of the same order, the resulting system of hydrodynamie equations (the Enskog–Euler system) is different from that for the Boltzmann equation. The existence and uniqueness theorem, in this case for the Enskog equation, is proven on the time interval independent of the small parameters. As $\epsilon \downarrow 0$, the solution of the Enskog equation tends to the Maxwellian whose fluid-dynamic parameters solve the Enskog–Euler system. As a by-product — the existence theorem for the Enskog–Euler system is obtained.