Model equations in the kinetic theory of gases

Abstract

A model is proposed, no less realistic in most respects than the usual ones, which leads to physical conclusions which are the exact opposites of the results in the literature. In particular, with the model all normal modes have normalizable eigenfunctions, and the eigenvalues are analytic functions of the wavenumber k for all k. No so called 'Knudsen modes' exist. Qualitative arguments are given to suggest that the difference results from the fact that the model operator, like the true Boltzmann collision operator, is unbounded, whereas the conventional model operators are bounded.