Global Diffusive Expansion of Boltzmann Equation in exterior Domain

TL;DR

This paper proves the global validity of the diffusive limit from Boltzmann equations to Navier-Stokes-Fourier system in exterior domains, overcoming key mathematical challenges with a novel splitting technique.

Contribution

It introduces a new $L^2-L^3-L^6$ splitting method to handle the lack of Poincare's inequality in unbounded exterior domains for Boltzmann to fluid dynamic limits.

Findings

Established global diffusive limit in exterior domains

Developed a new splitting technique for unbounded domains

Extended $L^2-L^ Infty$ framework to exterior settings

Abstract

The study of flows over an obstacle is one of the fundamental problems in fluids. In this paper we establish the global validity of the diffusive limit for the Boltzmann equations to the Navier-Stokes-Fourier system in an exterior domain. To overcome the well-known difficulty of the lack of Poincare's inequality in unbounded domain, we develop a new $L^2-L^3-L^6$ splitting to extend $L^2-L^\infty$ framework into the unbounded domain.