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Existence of homoenergetic affine flows for the Boltzmann equation

Research paper by Carlo Cercignani

Indexed on: 01 Dec '89Published on: 01 Dec '89Published in: Archive for Rational Mechanics and Analysis



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.