Existence of steady very weak solutions to Navier-Stokes equations with non-Newtonian stress tensors

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10441162" target="_blank" >RIV/00216208:11320/21:10441162 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Vk.SE_4gXE" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Vk.SE_4gXE</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2020.12.038" target="_blank" >10.1016/j.jde.2020.12.038</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Existence of steady very weak solutions to Navier-Stokes equations with non-Newtonian stress tensors

Popis výsledku v původním jazyce

We provide existence of very weak solutions and a-priori estimates for steady flows of non-Newtonian fluids when the right-hand sides are not in the natural existence class. This includes stress laws that depend non-linearly on the shear rate of the fluid like power-law fluids. To obtain the a-priori estimates we make use of a refined solenoidal Lipschitz truncation that preserves zero boundary values. We provide also estimates in (Muckenhoupt) weighted spaces which permit us to regain a duality pairing, which than can be used to prove existence. Our estimates are valid even in the presence of the convective term. They are obtained via a new comparison method that allows to &quot;cut out&quot; the singularities of the right hand side such that the skew symmetry of the convective term can be used for large parts of the right hand side. (C) 2020 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

Existence of steady very weak solutions to Navier-Stokes equations with non-Newtonian stress tensors

Popis výsledku anglicky

We provide existence of very weak solutions and a-priori estimates for steady flows of non-Newtonian fluids when the right-hand sides are not in the natural existence class. This includes stress laws that depend non-linearly on the shear rate of the fluid like power-law fluids. To obtain the a-priori estimates we make use of a refined solenoidal Lipschitz truncation that preserves zero boundary values. We provide also estimates in (Muckenhoupt) weighted spaces which permit us to regain a duality pairing, which than can be used to prove existence. Our estimates are valid even in the presence of the convective term. They are obtained via a new comparison method that allows to &quot;cut out&quot; the singularities of the right hand side such that the skew symmetry of the convective term can be used for large parts of the right hand side. (C) 2020 Elsevier Inc. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

—

Svazek periodika

279

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

36

Strana od-do

10-45

Kód UT WoS článku

000617287000002

EID výsledku v databázi Scopus

2-s2.0-85099625375