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dc.contributor.authorTran, Chuong Van
dc.contributor.authorYu, Xinwei
dc.identifier.citationTran , C V & Yu , X 2019 , ' A geometrical regularity criterion in terms of velocity profiles for the three-dimensional Navier-Stokes equations ' , Quarterly Journal of Mechanics & Applied Mathematics , vol. 72 , no. 4 , pp. 545–562 .
dc.identifier.otherPURE: 260958653
dc.identifier.otherPURE UUID: 3d0d1f36-6464-4547-bb9b-c4944c1cc30f
dc.identifier.otherORCID: /0000-0002-1790-8280/work/63046380
dc.identifier.otherScopus: 85076721504
dc.identifier.otherWOS: 000501742900008
dc.description.abstractIn this article, we present a new kind of regularity criteria for the global well-posedness problem of the three-dimensional Navier–Stokes equations in the whole space. The novelty of the new results is that they involve only the profiles of the magnitude of the velocity. One particular consequence of our theorem is as follows. If for every fixed t∈(0,T)⁠, the ‘large velocity’ region Ω:={(x,t)∣|u(x,t)|>C(q)||u||L3q−6}⁠, for some C(q) appropriately defined, shrinks fast enough as q↗∞⁠, then the solution remains regular beyond T⁠. We examine and discuss velocity profiles satisfying our criterion. It remains to be seen whether these profiles are typical of general Navier–Stokes flows.
dc.relation.ispartofQuarterly Journal of Mechanics & Applied Mathematicsen
dc.rights© The Authors, 2019. Published by Oxford University Press. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectQA Mathematicsen
dc.subjectQC Physicsen
dc.titleA geometrical regularity criterion in terms of velocity profiles for the three-dimensional Navier-Stokes equationsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Applied Mathematicsen
dc.description.statusPeer revieweden

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