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Cauchy theory and exponential stability for inhomogeneous boltzmann equation for hard potentials without cut-off

hal.structure.identifierLaboratoire de Mathématiques Jean Leray [LMJL]
dc.contributor.authorHérau, Frédéric
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorTonon, Daniela
hal.structure.identifierDépartement de Mathématiques et Applications - ENS Paris [DMA]
dc.contributor.authorTristani, Isabelle
dc.date.accessioned2018-03-19T09:44:47Z
dc.date.available2018-03-19T09:44:47Z
dc.date.issued2017
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17561
dc.language.isoenen
dc.subjectdissipativityen
dc.subjectexponential rate of convergenceen
dc.subjectBoltzmann equation without cut-offen
dc.subjecthard potentialsen
dc.subjectCauchy theoryen
dc.subjectspec- tral gapen
dc.subjectlong-time asymptoticen
dc.subject.ddc515en
dc.titleCauchy theory and exponential stability for inhomogeneous boltzmann equation for hard potentials without cut-offen
dc.typeDocument de travail / Working paper
dc.description.abstractenIn this paper, we investigate both the problems of Cauchy theory and exponential stability for the inhomogeneous Boltzmann equation without angular cutoff. We only deal with the physical case of hard potentials type interactions (with a moderate angular singularity). We prove a result of existence and uniqueness of solutions in a close-to-equilibrium regime for this equation in weighted Sobolev spaces with a polynomial weight, contrary to previous works on the subject, all developed with a weight prescribed by the equilibrium. It is the first result in this more physically relevant framework for this equation. Moreover, we prove an exponential stability for such a solution, with a rate as close as we want to the optimal rate given by the semigroup decay of the linearized equation.en
dc.identifier.citationpages48en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01599973en
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2018-03-19T09:18:27Z
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