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Large time behavior of the a priori bounds for the solutions to the spatially homogeneous Boltzmann equations with soft potentials.

dc.contributor.authorDesvillettes, Laurent
dc.contributor.authorMouhot, Clément
HAL ID: 1892
dc.date.accessioned2009-06-23T09:04:56Z
dc.date.available2009-06-23T09:04:56Z
dc.date.issued2007
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/391
dc.language.isoenen
dc.subjectuniform in timeen
dc.subjectregularity boundsen
dc.subjectmo- ment boundsen
dc.subjectsoft potentialsen
dc.subjectspatially homogeneousen
dc.subjectBoltzmann equationen
dc.subject.ddc519en
dc.titleLarge time behavior of the a priori bounds for the solutions to the spatially homogeneous Boltzmann equations with soft potentials.en
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherCMLA, École Normale Supérieure de Cachan;France
dc.description.abstractenWe consider the spatially homogeneous Boltzmann equation for regularized soft potentials and Grad's angular cutoff. We prove that uniform (in time) bounds in $L^1 ((1 + |v|^s)dv)$ and $H^k$ norms, $s, k \ge 0$ hold for its solution. The proof is based on the mixture of estimates of polynomial growth in time of those norms together with the quantitative results of relaxation to equilibrium in $L^1$ obtained by the so-called “entropy-entropy production” method in the context of dissipative systems with slowly growing a priori bounds (see reference [14]).en
dc.relation.isversionofjnlnameAsymptotic Analysis
dc.relation.isversionofjnlvol54en
dc.relation.isversionofjnlissue3-4en
dc.relation.isversionofjnldate2007
dc.relation.isversionofjnlpages235-245en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00079949/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherAmsterdam : IOS Pressen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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