On Blowup for Gain-Term-Only classical and relativistic Boltzmann equations

Andreasson, Hakan; Calogero, Simon; Illner, Reinhard

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On Blowup for Gain-Term-Only classical and relativistic Boltzmann equations

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Calogero, Simon
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Andreasson, H., Calogero, S., & Illner, R. (2004). On Blowup for Gain-Term-Only classical and relativistic Boltzmann equations. Mathematical Methods in the Applied Sciences, 27(18), 2231-2240.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5106-9

Abstract

We show that deletion of the loss part of the collision term in all physically relevant versions of the Boltzmann equation, including the relativistic case, will in general lead to blowup in finite time of a solution and hence prevent global existence. Our result corrects an error in the proof given in Ref. [12], where the result was announced for the classical hard sphere case; here we give a simpler proof which applies much more generally.