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December  2009, 2(4): 551-646. doi: 10.3934/krm.2009.2.551

A review of Boltzmann equation with singular kernels

Radjesvarane Alexandre 1,

1. 

Irenav, French Naval Academy, 29240 Brest Lanveoc-Poulmic, France

Received  September 2009 Revised  September 2009 Published  October 2009

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.
Keywords: hypoellipticity, singular kernels., existence, cutoff hypothesis, harmonic analysis, Boltzmann equations.
Mathematics Subject Classification: Primary: 42B25, 35Sxx; Secondary: 35Qx.
Citation: Radjesvarane Alexandre. A review of Boltzmann equation with singular kernels. Kinetic and Related Models, 2009, 2 (4) : 551-646. doi: 10.3934/krm.2009.2.551
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