Kinetic and Related Models (KRM)

A review of Boltzmann equation with singular kernels

Pages: 551 - 646, Volume 2, Issue 4, December 2009      doi:10.3934/krm.2009.2.551

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Radjesvarane Alexandre - Irenav, French Naval Academy, 29240 Brest Lanveoc-Poulmic, France (email)

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.

Keywords:  Boltzmann equations, cutoff hypothesis, existence, harmonic analysis, hypoellipticity, singular kernels.
Mathematics Subject Classification:  Primary: 42B25, 35Sxx; Secondary: 35Qxx.

Received: September 2009;      Revised: September 2009;      Available Online: October 2009.