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Local energy weak solutions for the Navier-Stokes equations in the half-space

hal.structure.identifierKyoto University
dc.contributor.authorMAEKAWA, Yasunori
hal.structure.identifierTokyo Institute of Technology [Tokyo] [TITECH]
dc.contributor.authorMIURA, Hideyuki
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPRANGE, Christophe
dc.date.accessioned2024-04-04T02:32:09Z
dc.date.available2024-04-04T02:32:09Z
dc.date.issued2019
dc.identifier.issn0010-3616
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190358
dc.description.abstractEnThe purpose of this paper is to prove the existence of global in time local energy weak solutions to the Navier-Stokes equations in the half-space R3+. Such solutions are sometimes called Lemari´e-Rieusset solutions in the whole space R3. The main tool in our work is an explicit representation formula for the pressure, which is decomposed into a Helmholtz-Leray part and a harmonic part due to the boundary. We also explain how our result enables to reprove the blow-up of the scale-critical L3(R3+) norm obtained by Barker and Seregin for solutions developing a singularity in finite time.
dc.description.sponsorshipBords, oscillations et couches limites dans les systèmes différentiels - ANR-16-CE40-0027
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enLocal energy weak solutions for the Navier-Stokes equations in the half-space
dc.typeArticle de revue
dc.identifier.doi10.1007/s00220-019-03344-4
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
dc.subject.halPhysique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
dc.identifier.arxiv1711.04486
bordeaux.journalCommunications in Mathematical Physics
bordeaux.page517–580
bordeaux.volume367
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01915527
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01915527v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20in%20Mathematical%20Physics&rft.date=2019&rft.volume=367&rft.issue=2&rft.spage=517%E2%80%93580&rft.epage=517%E2%80%93580&rft.eissn=0010-3616&rft.issn=0010-3616&rft.au=MAEKAWA,%20Yasunori&MIURA,%20Hideyuki&PRANGE,%20Christophe&rft.genre=article


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