A review of Boltzmann equation with singular kernels

Radjesvarane Alexandre

doi:10.3934/krm.2009.2.551

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2009, Volume 2, Issue 4: 551-646. Doi: 10.3934/krm.2009.2.551

This issue Previous Article Next Article Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation

A review of Boltzmann equation with singular kernels

Radjesvarane Alexandre^1,

1.
Irenav, French Naval Academy, 29240 Brest Lanveoc-Poulmic

Received: August 31, 2009

Revised: August 31, 2009

Published: November 2009

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Abstract

We review recent results about Boltzmann equation for singular or non cutoff cross-sections. Both spatially homogeneous and inhomogeneous Boltzmann equations are considered, and ideas related to Landau equation are explained. Various technical tools are presented, together with applications to existence and regularization issues.

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Mathematics Subject Classification: Primary: 42B25, 35Sxx; Secondary: 35Qxx.

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