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

TL;DR

This paper studies the analyticity and Gevrey regularity of solutions to the non-cutoff Boltzmann equation, providing sharp short-time estimates and global-in-time bounds using hypoelliptic estimates and macro-micro decomposition.

Contribution

It establishes the first sharp short-time and global-in-time radius estimates for the analyticity and Gevrey regularity of solutions to the non-cutoff Boltzmann equation.

Findings

Sharp short-time radius of analyticity and Gevrey regularity established.

Global-in-time radius estimates in Gevrey space obtained.

Combines hypoelliptic estimates with macro-micro decomposition techniques.

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.