dc.contributor.author Mouhot, Clément dc.contributor.author Strain, Robert dc.date.accessioned 2009-07-03T08:45:08Z dc.date.available 2009-07-03T08:45:08Z dc.date.issued 2007 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/720 dc.language.iso en en dc.subject linearized Boltzmann operator dc.subject linearized Landau operator dc.subject quantitative dc.subject long-range interaction dc.subject non-cutoff dc.subject soft potentials dc.subject spectral gap dc.subject coercivity estimates en dc.subject.ddc 519 en dc.title Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff en dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother University of Harvard;États-Unis dc.description.abstracten In this paper we prove new constructive coercivity estimates for the Boltzmann collision operator without cutoff, that is for long-range interactions. In particular we give a generalized sufficient condition for the existence of a spectral gap which involves both the growth behavior of the collision kernel at large relative velocities and its singular behavior at grazing and frontal collisions. It provides in particular existence of a spectral gap and estimates on it for interactions deriving from the hard potentials $\phi(r) = r^{-(s−1)}$, $s \ge 5$ or the so-called moderately soft potentials $\phi(r) = r^{−(s−1)}$, $3 < s < 5$, (without angular cutoff). In particular this paper recovers (by constructive means), improves and extends previous results of Pao [46]. We also obtain constructive coercivity estimates for the Landau collision operator for the optimal coercivity norm pointed out in [34] and we formulate a conjecture about a unified necessary and sufficient condition for the existence of a spectral gap for Boltzmann and Landau linearized collision operators. en dc.relation.isversionofjnlname Journal de Mathématiques Pures et Appliquées dc.relation.isversionofjnlvol 87 en dc.relation.isversionofjnlissue 5 en dc.relation.isversionofjnldate 2007-05 dc.relation.isversionofjnlpages 515-535 en dc.relation.isversionofdoi http://dx.doi.org/10.1016/j.matpur.2007.03.003 en dc.identifier.urlsite http://hal.archives-ouvertes.fr/hal-00086958/en/ en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher Elsevier en dc.subject.ddclabel Probabilités et Mathématiques appliquées en
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