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A remarkable estimate for the solutions of the Boltzmann equation. (English) Zbl 0762.35090

The author proves a global (in time) a priori bound for a certain moment of classical solutions of the Boltzmann equation. This moment contains the collision kernel. The assumptions are that the solution is one- dimensional in space, and that the collision kernel satisfies certain cut off properties. The proof uses the collision invariants and the \(H\)- theorem.
Reviewer: H.Lange (Köln)

MSC:

35Q35 PDEs in connection with fluid mechanics
45K05 Integro-partial differential equations
82C70 Transport processes in time-dependent statistical mechanics
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