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Hydrodynamic limits with shock waves of the Boltzmann equation

✍ Scribed by Shi-Hsien Yu

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
282 KB
Volume
58
Category
Article
ISSN
0010-3640

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✦ Synopsis

Abstract

We show that piecewise smooth solutions with shocks of the Euler equations in gas dynamics can be obtained as the zero Knudsen number limit of solutions of the Boltzmann equation for hard sphere collision model. The construction of the Boltzmann solutions is done in two steps. First we introduce a generalized Hilbert expansion with shock layer correction to construct approximations to the solutions of the Boltzmann equations with small Knudsen numbers. We then apply the recently developed macro‐micro decomposition and energy method for Boltzmann shock layers to construct the exact Boltzmann solutions through the stability analysis. © 2004 Wiley Periodicals, Inc.

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