Acoustic Limit of the Boltzmann Equation: Classical Solutions

We study the acoustic limit from the Boltzmann equation in the framework of classical solutions. For a solution Fε = μ+ε √ μfε to the rescaled Boltzmann equation in the acoustic time scaling ∂tFε + v·∇xFε = 1 ε Q(Fε, Fε) , inside a periodic box T, we establish the global-in-time uniform energy estimates of fε 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.