The regularity of discrete models of the Boltzmann equation
Yasushi Shizuta, Shuichi Kawashima · Proceedings of the Japan Academy Series A Mathematical Sciences · 1985
The aim of this note is to single out a category of the discrete Boltzmann equations as the regular models of the Boltzmann equation.It is shown that there exist regular models with n moduli of velocities for an arbitrary integer n_> 2.1. Let M={v, ...,v} be the set of velocities, i.e., the constant vectors in R. We assume that the linear span of M coincides with R. The model M is essentially three-dimensional in this sense.First of all, we introduce the notion of the collision.Let us denote by the set of all unordered pairs of distinct velocities.We may set Y={(vo v);