On the radius of analyticity and Gevrey regularity for the Boltzmann equation

Abstract: This paper investigates the non-cutoff Boltzmann equation for hard potentials in a perturbative setting. We first establish a sharp short-time estimate on the radius of analyticity and Gevrey regularity of mild solutions. Furthermore, we obtain a global-in-time radius estimate in Gevrey space. The proof combines hypoelliptic estimates with the macro-micro decomposition.