A remark on Cannone-Karch solutionsto the homogeneous Boltzmann equation for Maxwellian molecules

Yoshinori Morimoto

doi:10.3934/krm.2012.5.551

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2012, Volume 5, Issue 3: 551-561. Doi: 10.3934/krm.2012.5.551

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A remark on Cannone-Karch solutions to the homogeneous Boltzmann equation for Maxwellian molecules

Yoshinori Morimoto^1,

1.
Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, 606-8501

Received: December 31, 2011

Revised: February 29, 2012

Published: August 2012

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Abstract

The purpose of this paper is to extend the result concerning the existence and the uniqueness of infinite energy solutions, given by Cannone-Karch, of the Cauchy problem for the spatially homogeneous Boltzmann equation of Maxwellian molecules without Grad's angular cutoff assumption in the mild singularity case, to the strong singularity case. This extension follows from a simple observation of the symmetry on the unit sphere for the Bobylev formula which is the Fourier transform of the Boltzmann collision term.

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Mathematics Subject Classification: 35A05, 35B65, 35D10, 76P05, 82C40.

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References

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