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

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Date
2005
Link to item file
http://hal.archives-ouvertes.fr/hal-00087219/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
spectral gap ; Boltzmann linearized operator ; Landau linearized operator ; geometrical properties ; explicit ; grazing collision limit ; hard potentials
Journal issue
Revista Matematica Iberoamericana
Volume
21
Publication date
2005
Article pages
819-841
Publisher
Real Sociedad Matemática Española
URI
https://basepub.dauphine.fr/handle/123456789/374
Collections
  • CEREMADE : Publications
Metadata
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Author
Baranger, Céline
Mouhot, Clément
Type
Article accepté pour publication ou publié
Abstract (EN)
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.

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