Show simple item record

dc.contributor.authorCarrillo, Jose A.
dc.contributor.authorFerreira, Lucas C. F.
dc.contributor.authorPrecioso, Juliana C. [UNESP]
dc.identifier.citationAdvances In Mathematics. San Diego: Academic Press Inc. Elsevier B.V., v. 231, n. 1, p. 306-327, 2012.
dc.description.abstractWe consider a one dimensional transport model with nonlocal velocity given by the Hilbert transform and develop a global well-posedness theory of probability measure solutions. Both the viscous and non-viscous cases are analyzed. Both in original and in self-similar variables, we express the corresponding equations as gradient flows with respect to a free energy functional including a singular logarithmic interaction potential. Existence, uniqueness, self-similar asymptotic behavior and inviscid limit of solutions are obtained in the space P-2(R) of probability measures with finite second moments, without any smallness condition. Our results arc based on the abstract gradient flow theory developed by Ambrosio et al. (2005) [2]. An important byproduct of our results is that there is a unique, up to invariance and translations, global in time self-similar solution with initial data in P-2(R), which was already obtained by Deslippe etal. (2004) [17] and Biler et al. (2010) [6] by different methods. Moreover, this self-similar solution attracts all the dynamics in self-similar variables. The crucial monotonicity property of the transport between measures in one dimension allows to show that the singular logarithmic potential energy is displacement convex. We also extend the results to gradient flow equations with negative power-law locally integrable interaction potentials. (C) 2012 Elsevier B.V. All rights reserved.en
dc.description.sponsorshipMinisterio de Ciência e Innovacion
dc.description.sponsorshipAgencia de Gestio d'Ajuts Universitaris i de Recerca-Generalitat de Catalunya
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.publisherAcademic Press Inc. Elsevier B.V.
dc.relation.ispartofAdvances in Mathematics
dc.sourceWeb of Science
dc.subjectGradients flowsen
dc.subjectOptimal transporten
dc.subjectAsymptotic behavioren
dc.subjectInviscid limiten
dc.titleA mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocityen
dcterms.rightsHolderAcademic Press Inc. Elsevier B.V.
dc.contributor.institutionUniv Autonoma Barcelona
dc.contributor.institutionUniversidade Estadual de Campinas (UNICAMP)
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.description.affiliationUniv Autonoma Barcelona, ICREA, Bellaterra 08193, Barcelona, Spain
dc.description.affiliationUniv Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Barcelona, Spain
dc.description.affiliationUniv Estadual Campinas, IMECC, Dept Matemat, BR-13083859 Campinas, SP, Brazil
dc.description.affiliationUniv Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose do Rio Preto, SP, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose do Rio Preto, SP, Brazil
dc.rights.accessRightsAcesso restrito
dc.description.sponsorshipIdMICINN: MTM2011-27739-C04-02
dc.description.sponsorshipIdAgencia de Gestio d'Ajuts Universitaris i de Recerca-Generalitat de Catalunya: 2009-SGR-345
dc.description.sponsorshipIdCAPES: BEX2872/05-6
unesp.campusUniversidade Estadual Paulista (UNESP), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Pretopt
Localize o texto completo

Files in this item


There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record