# American Institute of Mathematical Sciences

September  2012, 5(3): 441-458. doi: 10.3934/krm.2012.5.441

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

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

Received  November 2011 Revised  February 2012 Published  August 2012

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.
Citation: Yong-Kum Cho. A quadratic Fourier representation of the Boltzmann collision operator with an application to the stability problem. Kinetic & Related Models, 2012, 5 (3) : 441-458. doi: 10.3934/krm.2012.5.441
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##### References:
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