Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials
Baranger, Céline; Mouhot, Clément (2005), Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials, Revista Matematica Iberoamericana, 21, p. 819-841
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00087219/en/
Journal nameRevista Matematica Iberoamericana
Real Sociedad Matemática Española
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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.
Subjects / Keywordsspectral gap ; Boltzmann linearized operator ; Landau linearized operator ; geometrical properties ; explicit ; grazing collision limit ; hard potentials
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