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Acoustic limit for the Boltzmann equation in optimal scaling
Author(s) -
Guo Yan,
Jiang Ning,
Jang Juhi
Publication year - 2010
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20308
Subject(s) - boltzmann equation , knudsen number , limit (mathematics) , mathematics , scaling , euler's formula , direct simulation monte carlo , scaling limit , euler equations , boltzmann constant , collision , mathematical analysis , compressibility , statistical physics , physics , mechanics , geometry , thermodynamics , statistics , computer science , computer security , dynamic monte carlo method , monte carlo method
Based on a recent L 2 − L ∞ framework, we establish the acoustic limit of the Boltzmann equation for general collision kernels. The scaling of the fluctuations with respect to the 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. © 2009 Wiley Periodicals, Inc.
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