On the regularity to the solutions of the Navier--Stokes equations via one velocity component

Result code in IS VaVaI

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Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On the regularity to the solutions of the Navier--Stokes equations via one velocity component

Original language description

We consider the regularity criteria for the incompressible Navier--Stokes equations connected with one velocity component. Based on the method from cite{CaTi} we prove that the weak solution is regular, provided $ u_3 in L^t(0,T; L^s(R^3))$, $frac 2t+frac 3s leq frac 34 + frac{1}{2s}$, $s} frac {10}{3} $ or provided $ nabla u_3 in L^t(0,T; L^s(R^3))$, $frac 2t +frac 3s leq frac{19}{12} + frac 1{2s}$ if $sin (frac{30}{19},3]$ or $frac 2t + frac 3s leq frac 32 + frac{3}{4s}$ if $sin (3,infty]$. As a corollary, we also improve the regularity criteria expressed by the regularity of $pder{p}{x_3}$ or $pder{u_3}{x_3}$.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2010

Confidentiality

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

Name of the periodical

Nonlinearity

ISSN

0951-7715

e-ISSN

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Volume of the periodical

23

Issue of the periodical within the volume

5

Country of publishing house

GB - UNITED KINGDOM

Number of pages

11

Pages from-to

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UT code for WoS article

000276728100004

EID of the result in the Scopus database

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