Global well-posedness in spatially critical Besov space for the Boltzmann equation

TL;DR

This paper establishes the existence and uniqueness of global solutions to the Boltzmann equation in a critical Besov space, using advanced harmonic analysis techniques to handle nonlinear collision terms.

Contribution

It introduces a novel approach to prove global well-posedness in a critical space for the Boltzmann equation, employing Littlewood-Paley theory for nonlinear estimates.

Findings

Global strong solution constructed in critical Besov space

New estimates for nonlinear collision term developed

Solution captures intrinsic properties of the Boltzmann equation

Abstract

The unique global strong solution in the Chemin-Lerner type space to the Cauchy problem on the Boltzmann equation for hard potentials is constructed in perturbation framework. Such solution space is of critical regularity with respect to spatial variable, and it can capture the intrinsic property of the Botlzmann equation. For the proof of global well-posedness, we develop some new estimates on the nonlinear collision term through the Littlewood-Paley theory.