The Boltzmann equation near a rotational local Maxwellian

TL;DR

This paper studies the Boltzmann equation in rotationally symmetric domains, proving global existence and convergence to a special equilibrium called the rotational local Maxwellian, which accounts for angular momentum.

Contribution

It establishes the first global well-posedness and convergence results for the Boltzmann equation near rotational local Maxwellians using an L2-L1 framework.

Findings

Proved global well-posedness of the Boltzmann equation near rotational Maxwellians.

Established convergence towards the rotational local Maxwellian equilibrium.

Extended the L2-L1 analytical framework to rotationally symmetric settings.

Abstract

In rotationally symmetric domains, the Boltzmann equation with specular reflection boundary condition has a special type of equilibrium states called the rotational local Maxwellian which, unlike the uniform Maxwellian, has an additional term related to the angular momentum of the gas. In this paper, we consider the initial boundary value problem of the Boltzmann equation near the rotational local Maxwellian. Based on the L2-L1 framework of [12], we establish the global well-posedness and the convergence toward such equilibrium states.