Acoustic Limit for the Boltzmann equation in Optimal Scaling

2009/01/15 by Yan Guo, Guo, Yan, Juhi Jang +3
Engineering · Mathematics · #76P05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.0901.2290

openalex publication_date 2009/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on a recent L²-L^∞ 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.

Citations

• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Symmetric hyperbolic linear differential equations

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