A refined estimate of Green's function for Boltzmann equation

The Green's function of the Boltzmann equation plays an important role in studying both nonlinear initial value problems and initial-boundary value problems [8,11]. In this paper, we obtain a refined estimate of Green's function to facilitate a quantitative study of the Boltzmann equation. Specifically, more detailed microscopic velocity information is revealed in our refined estimates, which proves useful in the initial-boundary value problems. The proof relies on an enhanced version of the mixture lemma.