Acoustic Limit for the Boltzmann equation in Optimal Scaling

TL;DR

This paper proves the optimal acoustic limit for the Boltzmann equation across general collision kernels, using a new analytical framework that refines the understanding of the transition from kinetic to fluid dynamics.

Contribution

It introduces a novel $L^{2}{-}L^{ abla}$ framework to establish the optimal scaling of fluctuations in the acoustic limit for the Boltzmann equation.

Findings

Established the acoustic limit for general collision kernels

Achieved optimal scaling of fluctuations with respect to Knudsen number

Provided refined estimates of Euler and acoustic solutions

Abstract

Based on a recent $L^{2}{-}L^{\infty}$ framework, we establish the acoustic limit of the Boltzmann equation for general collision kernels. The scaling of the fluctuations with respect to Knudsen number is optimal. Our approach is based on a new analysis of the compressible Euler limit of the Boltzmann equation, as well as refined estimates of Euler and acoustic solutions.