Abstract
An existence theorem is proved for homoenergetic affine flows described by the Boltzmann equation. The result complements the analysis of Truesdell and of Galkin on the moment equations for a gas of Maxwellian molecules. Existence of the distribution function is established here for a large class of molecular models (hard sphere and angular cut-off interactions). Some of the data lead to an implosion and infinite density in a finite time, in agreement with the physical picture of the associated flows; for the remaining set of data, global existence is shown to hold.
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Communicated by R. G. Muncaster
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Cercignani, C. Existence of homoenergetic affine flows for the Boltzmann equation. Arch. Rational Mech. Anal. 105, 377–387 (1989). https://doi.org/10.1007/BF00281497
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DOI: https://doi.org/10.1007/BF00281497