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On the well-posedness of the spatially homogeneous Boltzmann equation with a moderate angular singularity

dc.contributor.authorMouhot, Clément
HAL ID: 1892
dc.contributor.authorFournier, Nicolas
dc.date.accessioned2010-01-18T08:42:01Z
dc.date.available2010-01-18T08:42:01Z
dc.date.issued2009
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/2989
dc.language.isoenen
dc.subjectKantorovich-Rubinstein distanceen
dc.subjectBoltzmann equation without cutoffen
dc.subjectuniquenessen
dc.subjectWasserstein distanceen
dc.subjectlong-range interactionen
dc.subject.ddc519en
dc.titleOn the well-posedness of the spatially homogeneous Boltzmann equation with a moderate angular singularityen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherUniversité Paris XII Val de Marne;France
dc.description.abstractenWe prove an inequality on the Kantorovich-Rubinstein distance -which can be seen as a particular case of a Wasserstein metric- between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, but with a moderate angular singularity. Our method is in the spirit of [7]. We deduce some well-posedness and stability results in the physically relevant cases of hard and moderately soft potentials. In the case of hard potentials, we relax the regularity assumption of [6], but we need stronger assumptions on the tail of the distribution (namely some exponential decay). We thus obtain the first uniqueness result for measure initial data. In the case of moderately soft potentials, we prove existence and uniqueness assuming only that the initial datum has finite energy and entropy (for very moderately soft potentials), plus sometimes an additionnal moment condition. We thus improve significantly on all previous results, where weighted Sobolev spaces were involved.en
dc.relation.isversionofjnlnameCommunications in Mathematical Physics
dc.relation.isversionofjnlvol289
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2009-08
dc.relation.isversionofjnlpages803-824
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00220-009-0807-3
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00135991/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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