Acoustic Limit for the Boltzmann equation in Optimal Scaling

Details Acoustic Limit for the Boltzmann equation in Optimal Scaling Acoustic Limit for the Boltzmann equation in Optimal Scaling

2009-01-15

arxiv.org/abs/0901.2290v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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