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A geometrical regularity criterion in terms of velocity profiles for the three-dimensional Navier-Stokes equations
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dc.contributor.author | Tran, Chuong Van | |
dc.contributor.author | Yu, Xinwei | |
dc.date.accessioned | 2020-10-03T23:41:41Z | |
dc.date.available | 2020-10-03T23:41:41Z | |
dc.date.issued | 2019-11 | |
dc.identifier.citation | Tran , 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 . https://doi.org/10.1093/qjmam/hbz018 | en |
dc.identifier.issn | 0033-5614 | |
dc.identifier.other | PURE: 260958653 | |
dc.identifier.other | PURE UUID: 3d0d1f36-6464-4547-bb9b-c4944c1cc30f | |
dc.identifier.other | ORCID: /0000-0002-1790-8280/work/63046380 | |
dc.identifier.other | Scopus: 85076721504 | |
dc.identifier.other | WOS: 000501742900008 | |
dc.identifier.uri | https://hdl.handle.net/10023/20720 | |
dc.description.abstract | In 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.format.extent | 18 | |
dc.language.iso | eng | |
dc.relation.ispartof | Quarterly Journal of Mechanics & Applied Mathematics | en |
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 https://doi.org/10.1093/qjmam/hbz018 | en |
dc.subject | QA Mathematics | en |
dc.subject | QC Physics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject.lcc | QA | en |
dc.subject.lcc | QC | en |
dc.title | A geometrical regularity criterion in terms of velocity profiles for the three-dimensional Navier-Stokes equations | en |
dc.type | Journal article | en |
dc.description.version | Postprint | en |
dc.contributor.institution | University of St Andrews. Applied Mathematics | en |
dc.identifier.doi | https://doi.org/10.1093/qjmam/hbz018 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2020-10-04 |
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