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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2021

Confidentiality

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

Name of the periodical

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

—

Volume of the periodical

279

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

36

Pages from-to

10-45

UT code for WoS article

000617287000002

EID of the result in the Scopus database

2-s2.0-85099625375