Acoustic limit of the Boltzmann equation: Classical solutions

Abstract

We study the acoustic limit from the Boltzmann equation in the framework of classical solutions. For a solution Fe = μ+ε√μ fε to the rescaled Boltzmann equation in the acoustic time scaling ∂tFε+v·∇xFε=1/ εQ(Fε, Fε inside a periodic box T 3, we establish the global-in-time uniform energy estimates of f ε in ε and prove that fε converges strongly to f whose dynamics is governed by the acoustic system. The collision kernel Q includes hard-sphere interaction and inverse-power law with an angular cutoff.