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Localized minimizers of flat rotating gravitational systems

dc.contributor.authorFernandez, Javier
HAL ID: 744716
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.date.accessioned2009-07-04T08:50:49Z
dc.date.available2009-07-04T08:50:49Z
dc.date.issued2008
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/770
dc.language.isoenen
dc.subjectangular velocity
dc.subjectentropy
dc.subjectdiffusion limit
dc.subjectdrift-diffusion
dc.subjectHardy-Littlewood-Sobolev inequality
dc.subjectbounded solutions
dc.subjectcritical bifurcation parameter
dc.subjectrotation
dc.subjectmass
dc.subjectsymmetry breaking
dc.subjectlocalized minimizers
dc.subjectradial solutions
dc.subjectminimization
dc.subjectsolutions with compact support
dc.subjectStellar dynamicsen
dc.subjectgravitation
dc.subject.ddc519en
dc.titleLocalized minimizers of flat rotating gravitational systemsen
dc.typeArticle accepté pour publication ou publiéen_US
dc.description.abstractenWe study a two dimensional system in solid rotation at constant angular velocity driven by a self-consistent three dimensional gravitational field. We prove the existence of non symmetric stationary solutions of such a flat system in the rotating frame as long as the angular velocity does not exceed some critical value which depends on the mass. The solutions can be seen as stationary solutions of a kinetic equation with a relaxation-time collision kernel forcing the convergence to the polytropic gas solutions, or as stationary solutions of an extremely simplified drift-diffusion model, which is derived from the kinetic equation by formally taking a diffusion limit. In both cases, the solutions are critical points of a free energy functional, and can be seen as localized minimizers in an appropriate sense. Symmetry breaking occurs for small angular velocities.en
dc.relation.isversionofjnlnameAnnales de l'Institut Henri Poincaré. Analyse non linéaire
dc.relation.isversionofjnlvol25en
dc.relation.isversionofjnlissue6en
dc.relation.isversionofjnldate2008
dc.relation.isversionofjnlpages1043-1071en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.anihpc.2007.01.001en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00112165/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherElsevier Masson SAS.en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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