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Loeb solutions of the boltzmann equation
 Leif Arkeryd
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Existence problems for the Boltzmann equation constitute a main area of research within the kinetic theory of gases and transport theory. The present paper considers the spatially periodic case with L^{1} initial data. The main result is that the Loeb subsolutions obtained in a preceding paper are shown to be true solutions. The proof relies on the observation that monotone entropy and finite energy imply Loeb integrability of nonstandard approximate solutions, and uses estimates from the proof of the Htheorem. Two aspects of the continuity of the solutions are also considered.
 Anderson, R. M. (1976) A nonstandard representation for Brownian motion and Ito integration. Israel J. of Math. 25: pp. 1546
 Arkeryd, L. (1972) On the Boltzmann equation, Arch. Rational Mech. Anal. 45: pp. 134
 Arkeryd, L. (1981) A nonstandard approach to the Boltzmann equation. Arch. Rational Mech. Anal. 77: pp. 110
 C. Cercignani, Theory and application of the Boltzmann equation, Academic Press (1975).
 Cutland, N. J. (1983) Internal controls and relaxed controls. J. London Math. Soc. 27: pp. 130140
 Cutland, N. J. (1983) NonStandard measure theory and its applications. Bull. London Math. Soc. 15: pp. 529589
 Loeb, P. A. (1975) Conversion from nonstandard to standard measure spaces and applications in probability theory. Trans. Amer. Math. Soc. 211: pp. 113122
 C. Truesdell & R. G. Muncaster, Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas, Academic Press (1980).
 Title
 Loeb solutions of the boltzmann equation
 Journal

Archive for Rational Mechanics and Analysis
Volume 86, Issue 1 , pp 8597
 Cover Date
 19840301
 DOI
 10.1007/BF00280649
 Print ISSN
 00039527
 Online ISSN
 14320673
 Publisher
 SpringerVerlag
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 Authors

 Leif Arkeryd ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Chalmers University of Technology and the University of Göteborg, S41296, Göteborg, Sweden