Classification of equilibria for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles

TL;DR

This paper extends the classification of equilibrium solutions for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles from three dimensions to all dimensions greater than or equal to two, using geometric characterization results.

Contribution

It generalizes previous results by providing a classification for any dimension n ≥ 2, based on recent geometric characterizations of Euclidean balls.

Findings

Classification of equilibria for all n ≥ 2.

Extension of previous 3D results to higher dimensions.

Use of geometric characterization of Euclidean balls.

Abstract

The classification of equilibria for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles is proved for any $n$-dimensional velocity space with $n\ge 2$. The same classification has been proven in \cite{Lu2001} for $n=3$. Now the proof for $n\ge 2$ is based on a recent result on a characterization of Euclidean balls for all dimensions $\ge 2$.