On Cabannes' 32-velocity models of the Boltzmann equation (Q1091213)

The paper begins with a review of the regular (in the sense of \textit{Y. Shizuta} and \textit{S. Kawashima}, Proc. Japan Acad., Ser. A 61, 252-254 (1985; Zbl 0589.76098)) discrete velocity models of the Boltzmann equation. The main result of the present work is a proof of the regularity of Cabannes' 32-velocity models. As a consequence, these models satisfy a global existence, uniqueness and asymptotic stability theorem for the Cauchy problem with the initial values close to the absolute Maxwellian.