Analytical regularizing effect for the radial and spatially homogeneous Boltzmann equation

TL;DR

This paper proves that radial symmetric weak solutions to the spatially homogeneous Boltzmann equation without angular cutoff become analytic over time, highlighting a regularizing effect.

Contribution

It establishes the analyticity of solutions for the first time in the context of the non-cutoff Boltzmann equation with radial symmetry.

Findings

Radial symmetric weak solutions become analytic for positive time.

The regularizing effect occurs without angular cutoff assumptions.

Provides new insights into the solution behavior of the Boltzmann equation.

Abstract

In this paper, we consider a class of spatially homogeneous Boltzmann equation without angular cutoff. We prove that any radial symmetric weak solution of the Cauchy problem become analytic for positive time.