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hal.structure.identifierDepartment of Mathematics, Graduate School of Science
dc.contributor.authorHIGAKI, Mitsuo
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierCentre National de la Recherche Scientifique [CNRS]
dc.contributor.authorPRANGE, Christophe
dc.date.accessioned2024-04-04T02:58:41Z
dc.date.available2024-04-04T02:58:41Z
dc.date.issued2020
dc.identifier.issn0944-2669
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192678
dc.description.abstractEnWe investigate regularity estimates for the stationary Navier-Stokes equations above a highly oscillating Lipschitz boundary with the no-slip boundary condition. Our main result is an improved Lipschitz regularity estimate at scales larger than the boundary layer thickness. We also obtain an improved $C^{1,\mu}$ estimate and identify the building blocks of the regularity theory, dubbed `Navier polynomials'. In the case when some structure is assumed on the oscillations of the boundary, for instance periodicity, these estimates can be seen as local error estimates. Although we handle the regularity of the nonlinear stationary Navier-Stokes equations, our results do not require any smallness assumption on the solutions.
dc.description.sponsorshipBords, oscillations et couches limites dans les systèmes différentiels - ANR-16-CE40-0027
dc.description.sponsorshipEcoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure - ANR-18-CE40-0027
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enRegularity for the stationary Navier-Stokes equations over bumpy boundaries and a local wall law
dc.typeArticle de revue
dc.identifier.doi10.1007/s00526-020-01789-3
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.identifier.arxiv1911.12609
bordeaux.journalCalculus of Variations and Partial Differential Equations
bordeaux.page131
bordeaux.volume59
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue4
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-02388872
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02388872v1
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