Uniqueness of solutions to Boltzmann Equations

TL;DR

This paper proves the uniqueness of generalized and renormalized solutions to the Boltzmann Equation in Sobolev spaces using the Banach fixed point theorem, enhancing the mathematical understanding of these solutions.

Contribution

It extends the uniqueness results for Boltzmann Equation solutions to Sobolev spaces and includes renormalized solutions, using fixed point methods.

Findings

Uniqueness of generalized solutions established

Uniqueness of renormalized solutions proved

Application of Banach fixed point theorem to Boltzmann Equation

Abstract

By means of Banach fixed point theorem , the uniqueness of Boltzmann Equation generalizaled Solutions in Sobolev spaces in $L^1(\mathbb{R}^+\times \mathbb{R}^n\times \mathbb{R}^n)$, can be proved as well as Boltzmann Equation renormalized solutions uniqueness