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A regularity criterion for the Navier-Stokes equations via one diagonal entry of the velocity gradient

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F21%3A00365435" target="_blank" >RIV/68407700:21110/21:00365435 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.4310/CMS.2021.v19.n4.a10" target="_blank" >https://doi.org/10.4310/CMS.2021.v19.n4.a10</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.4310/CMS.2021.v19.n4.a10" target="_blank" >10.4310/CMS.2021.v19.n4.a10</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    A regularity criterion for the Navier-Stokes equations via one diagonal entry of the velocity gradient

  • Original language description

    We study the conditional regularity of solutions to the Navier-Stokes equations in the three dimensional space. Let u=(u(1),u(2),u(3)) denote the velocity. We impose an additional condition only on one diagonal entry of the velocity gradient, namely partial derivative(3)u(3), and show, using a technique based on the mixed multiplier theorem and an anisotropic version of the Troisi inequality, that if partial derivative(3)u(3) lies in the space L-beta(0,T;L-q) with suitable beta,q, then u is regular on (0,T]. Our result improves and extends the analogous results known from the literature.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10102 - Applied mathematics

Result continuities

  • Project

    <a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2021

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Communications in Mathematical Sciences

  • ISSN

    1539-6746

  • e-ISSN

  • Volume of the periodical

    19

  • Issue of the periodical within the volume

    4

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    12

  • Pages from-to

    1101-1112

  • UT code for WoS article

    000663345000010

  • EID of the result in the Scopus database

    2-s2.0-85117951656