Criteria for the regularity of the solutions to the Navier-Stokes equations based on the velocity gradient

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F15%3A00227609" target="_blank" >RIV/68407700:21110/15:00227609 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Criteria for the regularity of the solutions to the Navier-Stokes equations based on the velocity gradient

Popis výsledku v původním jazyce

We study the regularity of solutions to the Navier-Stokes equations in the whole three-dimensional space under the assumption that some additional conditions are imposed on one or more entries of the velocity gradient. Many such results with conditions using the Lebesgue spaces can be found in the literature, starting with the classical Beirao da Veiga's result. The main goal of the present paper is to generalize the known results by replacing the standard Lebesgue spaces by wider Besov spaces in spacevariables. In most such cases the technique of the proof leads to the deterioration of the Prodi-Serrin scale, so the results with the Besov spaces are not still quite satisfactory. Nevertheless, our technique leads to extensions and improvements of someresults from the literature.

Název v anglickém jazyce

Criteria for the regularity of the solutions to the Navier-Stokes equations based on the velocity gradient

Popis výsledku anglicky

We study the regularity of solutions to the Navier-Stokes equations in the whole three-dimensional space under the assumption that some additional conditions are imposed on one or more entries of the velocity gradient. Many such results with conditions using the Lebesgue spaces can be found in the literature, starting with the classical Beirao da Veiga's result. The main goal of the present paper is to generalize the known results by replacing the standard Lebesgue spaces by wider Besov spaces in spacevariables. In most such cases the technique of the proof leads to the deterioration of the Prodi-Serrin scale, so the results with the Besov spaces are not still quite satisfactory. Nevertheless, our technique leads to extensions and improvements of someresults from the literature.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Nonlinear Analysis: Theory, Methods & Applications

ISSN

0362-546X

e-ISSN

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Svazek periodika

118

Číslo periodika v rámci svazku

květen

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

21

Strana od-do

1-21

Kód UT WoS článku

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EID výsledku v databázi Scopus

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