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dc.contributor.authorMouhot, Clément
dc.contributor.authorStrain, Robert
dc.date.accessioned2009-07-03T08:45:08Z
dc.date.available2009-07-03T08:45:08Z
dc.date.issued2007
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/720
dc.language.isoenen
dc.subjectlinearized Boltzmann operator
dc.subjectlinearized Landau operator
dc.subjectquantitative
dc.subjectlong-range interaction
dc.subjectnon-cutoff
dc.subjectsoft potentials
dc.subjectspectral gap
dc.subjectcoercivity estimatesen
dc.subject.ddc519en
dc.titleSpectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoffen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversity of Harvard;États-Unis
dc.description.abstractenIn 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 $\phi(r) = r^{-(s&#8722;1)}$, $s \ge 5$ or the so-called moderately soft potentials $\phi(r) = r^{&#8722;(s&#8722;1)}$, $3 < s < 5$, (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.isversionofjnlnameJournal de Mathématiques Pures et Appliquées
dc.relation.isversionofjnlvol87en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2007-05
dc.relation.isversionofjnlpages515-535en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.matpur.2007.03.003en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00086958/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelProbabilités et Mathématiques appliquéesen


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