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Journal of Statistical Physics

, Volume 112, Issue 3–4, pp 629–655 | Cite as

Knudsen Layer for Gas Mixtures

  • Kazuo Aoki
  • Claude Bardos
  • Shigeru Takata
Article

Abstract

The Knudsen layer in rarefied gas dynamics is essentially described by a half-space boundary-value problem of the linearized Boltzmann equation, in which the incoming data are specified on the boundary and the solution is assumed to be bounded at infinity (Milne problem). This problem is considered for a binary mixture of hard-sphere gases, and the existence and uniqueness of the solution, as well as some asymptotic properties, are proved. The proof is an extension of that of the corresponding theorem for a single-component gas given by Bardos, Caflisch, and Nicolaenko [Comm. Pure Appl. Math.39:323 (1986)]. Some estimates on the convergence of the solution in a finite slab to the solution of the Milne problem are also obtained.

Knudsen layer gas mixtures Milne problem Boltzmann equation rarefied gas dynamics 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Kazuo Aoki
    • 1
  • Claude Bardos
    • 2
  • Shigeru Takata
    • 3
  1. 1.Department of Aeronautics and Astronautics, Graduate School of EngineeringKyoto UniversityKyotoJapan
  2. 2.Université Denis Diderot and LAN Université Pierre et Marie CurieParisFrance
  3. 3.Département de Mathématique et ApplicationsÉcole Normale SupérieureParis Cedex 05France

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