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Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Baranger, Céline 
Mouhot, Clément 

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.

Description

Keywords

math.AP, math.AP, math-ph, math.MP, 76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]

Journal Title

tica Iberoamericana

Conference Name

Journal ISSN

0213-2230

Volume Title

21

Publisher

European Mathematical Society - EMS - Publishing House