Exponential stability of an incompressible non-Newtonian fluid with delay

The existence and uniqueness of stationary solutions to an incompressible non-Newtonian fluid are first established. The exponential stability of steady-state solutions is then analyzed by means of four different approaches. The first is the classical Lyapunov function method, while the second one i...

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Detalles Bibliográficos
Autores: Liu, Linfang, Caraballo Garrido, Tomás, Fu, Xianlong
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2018
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/88961
Acceso en línea:https://hdl.handle.net/11441/88961
https://doi.org/10.3934/dcdsb.2018138
Access Level:acceso abierto
Palabra clave:Exponential stability
Stationary solution
Non-Newtonian fluids
Delay
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spelling Exponential stability of an incompressible non-Newtonian fluid with delayLiu, LinfangCaraballo Garrido, TomásFu, XianlongExponential stabilityStationary solutionNon-Newtonian fluidsDelayThe existence and uniqueness of stationary solutions to an incompressible non-Newtonian fluid are first established. The exponential stability of steady-state solutions is then analyzed by means of four different approaches. The first is the classical Lyapunov function method, while the second one is based on a Razumikhin type argument. Then, a method relying on the construction of Lyapunov functionals and another one using a Gronwall-like lemma are also exploited to study the stability, respectively. Some comments concerning several open research directions about this model are also included.Ministerio de Economía y Competitividad (MINECO). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Junta de AndalucíaNational Science Foundation of ChinaScience and Technology Commission of Shanghai MunicipalityShanghai Leading Academic Discipline ProjectAmerican Institute of Mathematical SciencesEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas Diferenciales2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/88961https://doi.org/10.3934/dcdsb.2018138reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete and Continuous Dynamical Systems - Series B, 23 (10), 4285-4303.MTM2015-63723-PP12-FQM-1492116711421137108713dz2260400B407https://www.aimsciences.org/article/doi/10.3934/dcdsb.2018138info:eu-repo/semantics/openAccessoai:idus.us.es:11441/889612026-06-17T12:51:07Z
dc.title.none.fl_str_mv Exponential stability of an incompressible non-Newtonian fluid with delay
title Exponential stability of an incompressible non-Newtonian fluid with delay
spellingShingle Exponential stability of an incompressible non-Newtonian fluid with delay
Liu, Linfang
Exponential stability
Stationary solution
Non-Newtonian fluids
Delay
title_short Exponential stability of an incompressible non-Newtonian fluid with delay
title_full Exponential stability of an incompressible non-Newtonian fluid with delay
title_fullStr Exponential stability of an incompressible non-Newtonian fluid with delay
title_full_unstemmed Exponential stability of an incompressible non-Newtonian fluid with delay
title_sort Exponential stability of an incompressible non-Newtonian fluid with delay
dc.creator.none.fl_str_mv Liu, Linfang
Caraballo Garrido, Tomás
Fu, Xianlong
author Liu, Linfang
author_facet Liu, Linfang
Caraballo Garrido, Tomás
Fu, Xianlong
author_role author
author2 Caraballo Garrido, Tomás
Fu, Xianlong
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
dc.subject.none.fl_str_mv Exponential stability
Stationary solution
Non-Newtonian fluids
Delay
topic Exponential stability
Stationary solution
Non-Newtonian fluids
Delay
description The existence and uniqueness of stationary solutions to an incompressible non-Newtonian fluid are first established. The exponential stability of steady-state solutions is then analyzed by means of four different approaches. The first is the classical Lyapunov function method, while the second one is based on a Razumikhin type argument. Then, a method relying on the construction of Lyapunov functionals and another one using a Gronwall-like lemma are also exploited to study the stability, respectively. Some comments concerning several open research directions about this model are also included.
publishDate 2018
dc.date.none.fl_str_mv 2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/88961
https://doi.org/10.3934/dcdsb.2018138
url https://hdl.handle.net/11441/88961
https://doi.org/10.3934/dcdsb.2018138
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete and Continuous Dynamical Systems - Series B, 23 (10), 4285-4303.
MTM2015-63723-P
P12-FQM-1492
11671142
11371087
13dz2260400
B407
https://www.aimsciences.org/article/doi/10.3934/dcdsb.2018138
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 American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical 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 15.300719

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