Abstract: Based on a recent L^{2}L^{&infin}; framework, we establish the acoustic limit of the Boltzmann equation for general collision kernels. For a solution , where , to the rescaled Boltzmann equation
in the whole space R^{3} or inside a periodic box T^{3}, we prove that G^{&epsilon}; converge to G whose dynamics is governed by the acoustic system, as δ = δ(ε), ε, ε/δ → 0. 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.
The results have been done in collaboration with Yan Guo and Ning Jiang.
