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Uniqueness and long time asymptotic for the parabolic-parabolic Keller-Segel equation

hal.structure.identifier
dc.contributor.authorCarrapatoso, Kleber*
hal.structure.identifier
dc.contributor.authorMischler, Stéphane*
dc.date.accessioned2013-11-02T11:35:28Z
dc.date.available2013-11-02T11:35:28Z
dc.date.issued2017
dc.identifier.issn0360-5302
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/11967
dc.language.isoenen
dc.subjectKeller-Segel system
dc.subjectlong-time behavior
dc.subjectstability
dc.subjectregularization
dc.subjectuniqueness
dc.subjectself-similar variables
dc.subject.ddc515en
dc.titleUniqueness and long time asymptotic for the parabolic-parabolic Keller-Segel equation
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherFacultad de Matematicas y Computacion Universidad de La Habana (CUBA);Cuba
dc.description.abstractenThe present paper deals with the parabolic-parabolic Keller-Segel equation in the plane inthe general framework of weak (or ``free energy") solutions associated to an initial datum with finite mass M<8π, finite second log-moment and finite entropy. The aim of the paper is twofold:(1) We prove the uniqueness of the ``free energy" solution. The proof uses a DiPerna-Lions renormalizing argument which makes possible to get the ``optimal regularity" as well as an estimate of the difference of two possible solutions in the critical L4/3 Lebesgue norm similarly as for the 2d vorticity Navier-Stokes equation. (2) We prove a radially symmetric and polynomial weighted L2 exponential stability of the self-similar profile in the quasi parabolic-elliptic regime. The proof is based on a perturbation argument which takes advantage of the exponential stability of the self-similar profile for the parabolic-elliptic Keller-Segel equation established in \cite{CamposDolbeault2012,EM}.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameCommunications in Partial Differential Equations
dc.relation.isversionofjnlvol42
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages291-345
dc.relation.isversionofdoi10.1080/03605302.2017.1280682
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01011361
dc.relation.isversionofjnlpublisherMarcel Dekker
dc.subject.ddclabelAnalyseen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-04-20T07:19:31Z
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