A quadratic Fourier representation of the Boltzmann collision operator with an application to thestability problem

Yong-Kum Cho

doi:10.3934/krm.2012.5.441

Article Contents

2012, Volume 5, Issue 3: 441-458. Doi: 10.3934/krm.2012.5.441

This issue Previous Article Next Article Hard sphere dynamics and the Enskog equation

A quadratic Fourier representation of the Boltzmann collision operator with an application to the stability problem

Yong-Kum Cho^1,

1.
Department of Mathematics, College of Natural Sciences, Chung-Ang University, 84 Heukseok-Ro, Dongjak-Gu, Seoul 156-756

Received: October 31, 2011

Revised: January 31, 2012

Published: August 2012

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Abstract

We present a Fourier transform formula of quadratic-form type for the collision operator with a Maxwellian kernel under the momentum transfer condition. As an application, we extend the work of Toscani and Villani on the uniform stability of the Cauchy problem for the associated Boltzmann equation to any physically relevant Maxwellian molecules in the long-range interactions with a minimal requirement for the initial data.

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Mathematics Subject Classification: 35Q82, 47G20, 76P05, 82B40.

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References

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