Acoustic Limit for the Boltzmann equation in Optimal Scaling

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.