Knudsen Layer for Gas Mixtures
 Kazuo Aoki,
 Claude Bardos,
 Shigeru Takata
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The Knudsen layer in rarefied gas dynamics is essentially described by a halfspace boundaryvalue 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 hardsphere 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 singlecomponent 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.
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 Title
 Knudsen Layer for Gas Mixtures
 Journal

Journal of Statistical Physics
Volume 112, Issue 34 , pp 629655
 Cover Date
 20030801
 DOI
 10.1023/A:1023876025363
 Print ISSN
 00224715
 Online ISSN
 15729613
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 Knudsen layer
 gas mixtures
 Milne problem
 Boltzmann equation
 rarefied gas dynamics
 Industry Sectors
 Authors

 Kazuo Aoki ^{(1)}
 Claude Bardos ^{(2)}
 Shigeru Takata ^{(3)}
 Author Affiliations

 1. Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto, 6068501, Japan
 2. Université Denis Diderot and LAN Université Pierre et Marie Curie, Paris, France
 3. Département de Mathématique et Applications, École Normale Supérieure, 45, rue d'Ulm, 75230, Paris Cedex 05, France