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Preprint 2009-025

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

tFε+vxFε−1Q(Fε,Fε),

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.

Paper:
Available as PDF (194 Kbytes).
Author(s):
Juhi Jang,
Ning Jiang,
Publishing information:
Accepted by Discrete and Continuous Dynamical Systems – Series A.
Also available as arXiv:0904.4459v1.
Comments:
Submitted by:
; 2009-05-12.