Plane Wave Propagation in Kinetic Theory

Abstract

A number of results for plane wave propagation in kinetic theory are obtained. Among these are the following. It is shown that the Boltzmann equation for bounded collision operator has a cutoff frequency beyond which plane waves cease to exist. The analytic continuation of the dispersion relation is discussed and asymptotic results beyond the critical frequency are obtained. Using a kinetic model it is shown that the low-frequency formal power series for complex wavenumber in terms of frequency (and vice versa) are divergent. The last is contrary to the recent result obtained for the rigid sphere Boltzmann equation.