Acoustic limit of the Boltzmann equation: Classical solutions
Juhi Jang and Ning Jiang
Abstract: 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
inside a periodic box T3, 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.