On the gain of regularity for the positive part of Boltzmann collision operator associated with soft-potentials

Yong-Kum Cho; Hera Yun

doi:10.3934/krm.2012.5.769

Article Contents

2012, Volume 5, Issue 4: 769-786. Doi: 10.3934/krm.2012.5.769

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On the gain of regularity for the positive part of Boltzmann collision operator associated with soft-potentials

Yong-Kum Cho^1, and
Hera Yun^1,

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

Received: January 31, 2012

Revised: April 30, 2012

Published: November 2012

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Abstract

As for the positive part of Boltzmann's collision operator associated with the collision kernel of soft-potential type, we evaluate its Fourier transform explicitly and prove a set of bilinear estimates for $L^p$ and Sobolev regularity.

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

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References

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