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December, 2005 Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials
Céline Baranger, Clément Mouhot
Rev. Mat. Iberoamericana 21(3): 819-841 (December, 2005).

Abstract

This paper deals with explicit spectral gap estimates for the linearized Boltzmann operator with hard potentials (and hard spheres). We prove that it can be reduced to the Maxwellian case, for which explicit estimates are already known. Such a method is constructive, does not rely on Weyl's Theorem and thus does not require Grad's splitting. The more physical idea of the proof is to use geometrical properties of the whole collision operator. In a second part, we use the fact that the Landau operator can be expressed as the limit of the Boltzmann operator as collisions become grazing in order to deduce explicit spectral gap estimates for the linearized Landau operator with hard potentials.

Citation

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Céline Baranger. Clément Mouhot. "Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials." Rev. Mat. Iberoamericana 21 (3) 819 - 841, December, 2005.

Information

Published: December, 2005
First available in Project Euclid: 11 January 2006

zbMATH: 1092.76057
MathSciNet: MR2231011

Subjects:
Primary: 76P05
Secondary: 82B40 , 82C40 , 82D05

Keywords: explicit , geometrical properties , grazing collision limit , Hard potentials , Landau linearized operator , linearized Boltzmann operator , spectral gap

Rights: Copyright © 2005 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.21 • No. 3 • December, 2005
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