Asymptotic analysis of the linearized Boltzmann collision operator from angular cutoff to non-cutoff

Abstract

We give quantitative estimates on the asymptotics of the linearized Boltzmann collision operator and its associated equation from angular cutoff to non-cutoff. On one hand, the results disclose the link between the hyperbolic property resulting from Grad’s cutoff assumption and the smoothing property due to the long-range interaction. On the other hand, with the help of localization techniques in phase space, we observe some new phenomena in the asymptotic limit process.