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The Boltzmann equation: Global existence for a rare gas in an infinite vacuum

Solutions of the Boltzmann equation are proved to exist, globally in time, under conditions that include the case of a finite volume of gas in an infinite vacuum when the mean free path of the gas is large enough. It is also proved, as might be expected in this case, that the density of the gas at each point in space goes to zero as time goes to infinity.

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1. Babovsky, H.: Randbedingungen in der kinetischen Theorie und Lösungen der Boltzmann-Gleichung. Ph. D. Dissertation, Universität Kaiserslautern 1983

2. Hamdache, K.: Existence globale et comportement asymptotique pour l'equation de Boltzmann à repartition discrète de vitesses. To appear in Journal de Méc. Th. et Appl.

3. Illner, R.: The Broadwell model for initial values inL ¹₊ (R). Commun. Math. Phys.93, 341–353 (1984)

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5. Tartar, L.: Some existence theorems for semilinear hyperbolic systems in one space variable. MRC Technical Summary Report, Madison 1980

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1. University of Kaiserslautern, D-6570, Kaiserslautern, Federal Republic of Germany

   Reinhard Illner

2. Department of Mathematics, University of Victoria, V8W 2Y2, B.C., Canada

   Marvin Shinbrot

1. Reinhard Illner
2. Marvin Shinbrot

Communicated by J. L. Lebowitz

Research supported by the Natural Science and Engineering Research Council Canada under Grant No. A-8560

Illner, R., Shinbrot, M. The Boltzmann equation: Global existence for a rare gas in an infinite vacuum. Commun.Math. Phys. 95, 217–226 (1984). https://doi.org/10.1007/BF01468142

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• Received: 31 January 1984

• Issue Date: June 1984

• DOI: https://doi.org/10.1007/BF01468142

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