The Boltzmann equation with non-isothermal Maxwell boundary conditions

TL;DR

This paper analyzes the Boltzmann equation with non-isothermal Maxwell boundary conditions, establishing the existence, uniqueness, and stability of steady states near the hydrodynamic limit in bounded domains.

Contribution

It provides the first rigorous proof of steady state existence and stability for the Boltzmann equation with non-isothermal boundary conditions.

Findings

Existence of a non-equilibrium steady state under small boundary temperature fluctuations

Uniqueness of the steady state in the near-hydrodynamic regime

Asymptotic stability of the steady state

Abstract

In this paper, we study the Boltzmann equation in a close to the hydrodynamic limit regime, set in bounded spatial domains with non-isothermal Maxwell boundary conditions. We establish the existence, uniqueness, and asymptotic stability of a non-equilibrium steady state under suitable smallness assumption on the temperature fluctuations at the boundary.