Cauchy problem to the homogeneous Boltzmann equation with Debye-Yukawa potential for measure initial datum

TL;DR

This paper establishes the existence, uniqueness, and smoothing effects of solutions to the homogeneous Boltzmann equation with Debye-Yukawa potential, starting from measure-valued initial data.

Contribution

It provides the first rigorous analysis of the Cauchy problem for this specific potential with measure initial data, including well-posedness and regularity results.

Findings

Existence of solutions under measure initial data

Uniqueness of solutions in the considered setting

Smoothing properties of solutions over time

Abstract

In this work, we prove the existence, uniqueness and smoothing properties of the solution to the Cauchy problem for the spatially homogeneous Boltzmann equation with Debye-Yukawa potential for probability measure initial datum.