Transport coefficients in the $2$-dimensional Boltzmann equation

Alexander Bobylev; Raffaele Esposito

doi:10.3934/krm.2013.6.789

Article Contents

2013, Volume 6, Issue 4: 789-800. Doi: 10.3934/krm.2013.6.789

This issue Previous Article Stability of a Vlasov-Boltzmann binary mixture at the phase transition on an interval Next Article On self-similar solutions to the homogeneous Boltzmann equation

Transport coefficients in the $2$-dimensional Boltzmann equation

Alexander Bobylev^1, and
Raffaele Esposito^2,

1.
Department of Mathematics, Karlstad University, SE-651 88 Karlstad
2.
International Research Center M&MOCS, Università di L'Aquila, Cisterna di Latina, 04012

Received: June 30, 2013

Revised: July 31, 2013

Published: November 2013

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Abstract

We show that a rarefied system of hard disks in a plane, described in the Boltzmann-Grad limit by the $2$-dimensional Boltzmann equation, has bounded transport coefficients. This is proved by showing opportune compactness properties of the gain part of the linearized Boltzmann operator.

Keywords:

Boltzmann equation,
transport coefficients.

Mathematics Subject Classification: 76P05, 82C40, 76A20.

Citation:

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