Density-dependent incompressible fluids with non-Newtonian viscosity

We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of pcoercivity and (p − 1)-growth, for a give...

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Author: Guillén González, Francisco Manuel
Format: article
Status:Published version
Publication Date:2004
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41239
Online Access:http://hdl.handle.net/11441/41239
https://doi.org/10.1007/s10587-004-6414-8
Access Level:Open access
Keyword:variable density
shear-dependent viscosity
power law
Carreau’s laws
weak solution
strong solution
periodic boundary conditions
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spelling Density-dependent incompressible fluids with non-Newtonian viscosityGuillén González, Francisco Manuelvariable densityshear-dependent viscositypower lawCarreau’s lawsweak solutionstrong solutionperiodic boundary conditionsWe study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of pcoercivity and (p − 1)-growth, for a given parameter p > 1. The existence of Dirichlet weak solutions was obtained in [2], in the cases p > 12/5 if d = 3 or p > 2 if d = 2, d being the dimension of the domain. In this paper, with help of some new estimates (which lead to point-wise convergence of the velocity gradient), we obtain the existence of space-periodic weak solutions for all p > 2. In addition, we obtain regularity properties of weak solutions whenever p > 20/9 (if d = 3) or p > 2 (if d = 2). Further, some extensions of these results to more general stress tensors or to Dirichlet boundary conditions (with a Newtonian tensor large enough) are obtained.Comisión Interministerial de Ciencia y TecnologíaInstitute of Mathematics, Czech Academy of SciencesEcuaciones Diferenciales y Análisis NuméricoComisión Interministerial de Ciencia y Tecnología (CICYT). España2004info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/41239https://doi.org/10.1007/s10587-004-6414-8reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésnullMAR98-0486http://dx.doi.org/10.1007/s10587-004-6414-8info:eu-repo/semantics/openAccessoai:idus.us.es:11441/412392026-06-17T12:51:07Z
dc.title.none.fl_str_mv Density-dependent incompressible fluids with non-Newtonian viscosity
title Density-dependent incompressible fluids with non-Newtonian viscosity
spellingShingle Density-dependent incompressible fluids with non-Newtonian viscosity
Guillén González, Francisco Manuel
variable density
shear-dependent viscosity
power law
Carreau’s laws
weak solution
strong solution
periodic boundary conditions
title_short Density-dependent incompressible fluids with non-Newtonian viscosity
title_full Density-dependent incompressible fluids with non-Newtonian viscosity
title_fullStr Density-dependent incompressible fluids with non-Newtonian viscosity
title_full_unstemmed Density-dependent incompressible fluids with non-Newtonian viscosity
title_sort Density-dependent incompressible fluids with non-Newtonian viscosity
dc.creator.none.fl_str_mv Guillén González, Francisco Manuel
author Guillén González, Francisco Manuel
author_facet Guillén González, Francisco Manuel
author_role author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
Comisión Interministerial de Ciencia y Tecnología (CICYT). España
dc.subject.none.fl_str_mv variable density
shear-dependent viscosity
power law
Carreau’s laws
weak solution
strong solution
periodic boundary conditions
topic variable density
shear-dependent viscosity
power law
Carreau’s laws
weak solution
strong solution
periodic boundary conditions
description We study the system of PDEs describing unsteady flows of incompressible fluids with variable density and non-constant viscosity. Indeed, one considers a stress tensor being a nonlinear function of the symmetric velocity gradient, verifying the properties of pcoercivity and (p − 1)-growth, for a given parameter p > 1. The existence of Dirichlet weak solutions was obtained in [2], in the cases p > 12/5 if d = 3 or p > 2 if d = 2, d being the dimension of the domain. In this paper, with help of some new estimates (which lead to point-wise convergence of the velocity gradient), we obtain the existence of space-periodic weak solutions for all p > 2. In addition, we obtain regularity properties of weak solutions whenever p > 20/9 (if d = 3) or p > 2 (if d = 2). Further, some extensions of these results to more general stress tensors or to Dirichlet boundary conditions (with a Newtonian tensor large enough) are obtained.
publishDate 2004
dc.date.none.fl_str_mv 2004
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/41239
https://doi.org/10.1007/s10587-004-6414-8
url http://hdl.handle.net/11441/41239
https://doi.org/10.1007/s10587-004-6414-8
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv null
MAR98-0486
http://dx.doi.org/10.1007/s10587-004-6414-8
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Institute of Mathematics, Czech Academy of Sciences
publisher.none.fl_str_mv Institute of Mathematics, Czech Academy of Sciences
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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