On the Euler Equation in Discrete Kinetic Theory

Abstract

The aim of this note is to investigate some mathematical structure of the Euler equation derived from the discrete Boltzmann equation as the first order approximation of the Chapman-Enskog expansion. The analysis developed in this article would be a basis for the study of nonlinear waves in discrete kinetic theory (cf. [2,7,3] for shock waves, [10] for rarefaction waves, and [6] for diffusion waves).