Diffusive Expansion of the Boltzmann equation for the flow past an obstacle

TL;DR

This paper proves the validity of a diffusive expansion from the Boltzmann equation to the Navier-Stokes-Fourier system in an exterior domain, using an $L^3-L^6$ framework, up to a critical time.

Contribution

It establishes the diffusive expansion for the Boltzmann equation in exterior domains with passing flow, extending previous results to unbounded domains with new analytical techniques.

Findings

Valid diffusive expansion up to critical time

Application of $L^3-L^6$ framework in exterior domains

Extension to non-zero passing flow scenarios

Abstract

The exterior domain problem is essential in fluid and kinetic equations. In this paper, we establish the validity of the diffusive expansion for the Boltzmann equations to the Navier-Stokes-Fourier system up to the critical time in an exterior domain with non-zero passing flow. We apply the $L^3-L^6$ framework to the unbounded domain in this paper.