Asymptotic behavior of linearized Boltzmann equations for soft potentials with cut-off

Abstract

We consider the asymptotic behavior of the linearized Boltzmann equation for soft potentials with cut-off. By introducing a new decomposition of the linearized Boltzmann operator, we analyze the spectrum of the linearized Boltzmann operator and obtain the asymptotic behaviors of the linearized Boltzmann equation for γ in (-3,0), extending the result in [12] for γ in (-1,0).