Gevrey Regularizing Effect for Solutions of the Non-Cutoff Boltzmann Equation in a Particular Case of Soft Potential with Critical Singularity

TL;DR

This paper demonstrates that solutions to the non-cutoff Boltzmann equation with a specific soft potential and critical singularity exhibit Gevrey regularity, indicating enhanced smoothness properties under these conditions.

Contribution

It establishes the Gevrey regularizing effect for solutions of the non-cutoff Boltzmann equation in a particular soft potential case with critical singularity s=1/2.

Findings

Solutions gain Gevrey regularity over time

Regularizing effect occurs in both spatially homogeneous and inhomogeneous cases

Results apply specifically to the case with critical singularity s=1/2

Abstract

In this paper we show the Gevrey regularizing effect of solutions to the non-cutoff spatially homogeneous and inhomogeneous Boltzmann equation for a particular soft potential with critical singularity s=1/2.