Some contributions to the study of incompressible micropolar fluids in two dimensional domains
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/39264 |
Resumo: | This thesis deals with some theoretical aspects related to the two-dimensional incompressible micropolar fluids model. In particular, two problems were addressed. The first of them is known in the literature as the initialization problem. The fundamental idea of this type of problem is to recover information from the initial data based on observations of the state of the system. For this purpose, a bounded and smooth domain of R2 with Dirichlet boundary conditions was considered. Optimal control theory techniques ensure the existence of at least one and at most a finite number of solutions for the problem. We also provide sufficient conditions to guarantee uniqueness of the solution. The second problem was the study of well posedness, in Hadamard’s sense, for the micropolar model with partial viscosity and singular initial data, including the possibility of measures as initial data in Morrey spaces. Through integral techniques and compactness arguments, the existence of a weak solution was established. Uniqueness and stability of these solutions were also analyzed, showing the model to be well posed. |
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CUNHA, Cleyton Natanael Lopes de Carvalhohttp://lattes.cnpq.br/6802995853570591http://lattes.cnpq.br/3205167619554233BRAZ E SILVA, Pablo Gustavo Albuquerque2021-02-22T18:26:01Z2021-02-22T18:26:01Z2020-12-22CUNHA, Cleyton Natanael Lopes de Carvalho. Some contributions to the study of incompressible micropolar fluids in two dimensional domains. 2020. Tese (Doutorado em Matemática) - Universidade Federal de Pernambuco, Recife, 2020.https://repositorio.ufpe.br/handle/123456789/39264This thesis deals with some theoretical aspects related to the two-dimensional incompressible micropolar fluids model. In particular, two problems were addressed. The first of them is known in the literature as the initialization problem. The fundamental idea of this type of problem is to recover information from the initial data based on observations of the state of the system. For this purpose, a bounded and smooth domain of R2 with Dirichlet boundary conditions was considered. Optimal control theory techniques ensure the existence of at least one and at most a finite number of solutions for the problem. We also provide sufficient conditions to guarantee uniqueness of the solution. The second problem was the study of well posedness, in Hadamard’s sense, for the micropolar model with partial viscosity and singular initial data, including the possibility of measures as initial data in Morrey spaces. Through integral techniques and compactness arguments, the existence of a weak solution was established. Uniqueness and stability of these solutions were also analyzed, showing the model to be well posed.Esta tese trata de alguns aspectos teóricos relacionados ao modelo bidimensional para fluidos micropolares incompressíveis. Em particular, foram abordados dois problemas. O primeiro deles é conhecido na literatura como problema de inicialização. A ideia fundamental desse tipo de problema é partindo de observações do estado do sistema, buscar recuperar informações dos dados iniciais. Para tanto, foi considerado um domínio suave e limitado do R2 com condições de Dirichlet na fronteira. Através de técnicas da teoria de controle ótimo, assegura-se a existência de pelo menos uma e no máximo uma quantidade finita de soluções para o problema. Também foram estudadas condições suficientes para garantir a unicidade de solução. O segundo problema foi dedicado ao estudo da boa colocação, no sentido de Hadamard, para o modelo micropolar com viscosidade parcial e dados iniciais singulares, incluindo a possibilidade de medidas como dados iniciais em espaços de Morrey. Por meio de técnicas integrais e argumentos de compacidade foi estabelecida a existência de solução fraca. A unicidade e a estabilidade dessas soluções também foram analisadas, concluindo que o modelo é bem-posto.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em MatematicaUFPEBrasilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/embargoedAccessAnáliseFluidos micropolaresProblema de inicializaçãoDados iniciais singularesSome contributions to the study of incompressible micropolar fluids in two dimensional domainsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETEXTTESE Cleyton Natanael Lopes de Carvalho Cunha.pdf.txtTESE Cleyton Natanael Lopes de Carvalho Cunha.pdf.txtExtracted texttext/plain131419https://repositorio.ufpe.br/bitstream/123456789/39264/4/TESE%20Cleyton%20Natanael%20Lopes%20de%20Carvalho%20Cunha.pdf.txtdfad2b83f79f92e68cac05c377684f56MD54THUMBNAILTESE Cleyton Natanael Lopes de Carvalho Cunha.pdf.jpgTESE Cleyton Natanael Lopes de Carvalho Cunha.pdf.jpgGenerated Thumbnailimage/jpeg1209https://repositorio.ufpe.br/bitstream/123456789/39264/5/TESE%20Cleyton%20Natanael%20Lopes%20de%20Carvalho%20Cunha.pdf.jpgfbf3bb4f0d0255eb25a33e4cb6cbb569MD55ORIGINALTESE Cleyton Natanael Lopes de Carvalho Cunha.pdfTESE Cleyton Natanael Lopes de Carvalho Cunha.pdfapplication/pdf727469https://repositorio.ufpe.br/bitstream/123456789/39264/1/TESE%20Cleyton%20Natanael%20Lopes%20de%20Carvalho%20Cunha.pdf3b21c24a8573954885344de82cf3d7dbMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv |
Some contributions to the study of incompressible micropolar fluids in two dimensional domains |
title |
Some contributions to the study of incompressible micropolar fluids in two dimensional domains |
spellingShingle |
Some contributions to the study of incompressible micropolar fluids in two dimensional domains CUNHA, Cleyton Natanael Lopes de Carvalho Análise Fluidos micropolares Problema de inicialização Dados iniciais singulares |
title_short |
Some contributions to the study of incompressible micropolar fluids in two dimensional domains |
title_full |
Some contributions to the study of incompressible micropolar fluids in two dimensional domains |
title_fullStr |
Some contributions to the study of incompressible micropolar fluids in two dimensional domains |
title_full_unstemmed |
Some contributions to the study of incompressible micropolar fluids in two dimensional domains |
title_sort |
Some contributions to the study of incompressible micropolar fluids in two dimensional domains |
author |
CUNHA, Cleyton Natanael Lopes de Carvalho |
author_facet |
CUNHA, Cleyton Natanael Lopes de Carvalho |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/6802995853570591 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/3205167619554233 |
dc.contributor.author.fl_str_mv |
CUNHA, Cleyton Natanael Lopes de Carvalho |
dc.contributor.advisor1.fl_str_mv |
BRAZ E SILVA, Pablo Gustavo Albuquerque |
contributor_str_mv |
BRAZ E SILVA, Pablo Gustavo Albuquerque |
dc.subject.por.fl_str_mv |
Análise Fluidos micropolares Problema de inicialização Dados iniciais singulares |
topic |
Análise Fluidos micropolares Problema de inicialização Dados iniciais singulares |
description |
This thesis deals with some theoretical aspects related to the two-dimensional incompressible micropolar fluids model. In particular, two problems were addressed. The first of them is known in the literature as the initialization problem. The fundamental idea of this type of problem is to recover information from the initial data based on observations of the state of the system. For this purpose, a bounded and smooth domain of R2 with Dirichlet boundary conditions was considered. Optimal control theory techniques ensure the existence of at least one and at most a finite number of solutions for the problem. We also provide sufficient conditions to guarantee uniqueness of the solution. The second problem was the study of well posedness, in Hadamard’s sense, for the micropolar model with partial viscosity and singular initial data, including the possibility of measures as initial data in Morrey spaces. Through integral techniques and compactness arguments, the existence of a weak solution was established. Uniqueness and stability of these solutions were also analyzed, showing the model to be well posed. |
publishDate |
2020 |
dc.date.issued.fl_str_mv |
2020-12-22 |
dc.date.accessioned.fl_str_mv |
2021-02-22T18:26:01Z |
dc.date.available.fl_str_mv |
2021-02-22T18:26:01Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
CUNHA, Cleyton Natanael Lopes de Carvalho. Some contributions to the study of incompressible micropolar fluids in two dimensional domains. 2020. Tese (Doutorado em Matemática) - Universidade Federal de Pernambuco, Recife, 2020. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/39264 |
identifier_str_mv |
CUNHA, Cleyton Natanael Lopes de Carvalho. Some contributions to the study of incompressible micropolar fluids in two dimensional domains. 2020. Tese (Doutorado em Matemática) - Universidade Federal de Pernambuco, Recife, 2020. |
url |
https://repositorio.ufpe.br/handle/123456789/39264 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/embargoedAccess |
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http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
embargoedAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Matematica |
dc.publisher.initials.fl_str_mv |
UFPE |
dc.publisher.country.fl_str_mv |
Brasil |
publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
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