{"id":{"repo_id":"brazil-ufpe","oai_identifier":"oai:repositorio.ufpe.br:123456789/31009"},"canonical_url":"https://search.dev.ndltd.org/etd/brazil-ufpe/oai:repositorio.ufpe.br:123456789/31009","repository":{"repo_id":"brazil-ufpe","name":"Brazil UFPE","base_url":"https://repositorio.ufpe.br/oai/request"},"display":{"title":"L² decay for weak solutions of the micropolar equations on R³","abstract":"We obtain decay estimates for solutions of the micropolar fluid equations . Such equations, proposed by A. C. Eringen, generalize the classic model of Navier-Stokes and describe the behavior of fluids with microstructure such as animal blood, liquid crystals, suspensions, among others. For this, we use a method developed by M. Schonbek, known by Fourier Splitting Method. In order to present the method, we first show how it was applied in the context of parabolic conservation laws and the Navier-Stokes equations to obtain decay estimates. Having done this, assuming the existence for solutions of the micropolar fluid system with Dirichlet conditions at infinity and we show the result when the external forces are either null or decay at an appropriate rate. Lastly, through retarded mollifiers and approximate solutions, we guarantee the existence of solutions for the micropolar fluidequations in convenient functional spaces and we prove the desired decay bound.","abstract_html":"We obtain decay estimates for solutions of the micropolar fluid equations . Such equations, proposed by A. C. Eringen, generalize the classic model of Navier-Stokes and describe the behavior of fluids with microstructure such as animal blood, liquid crystals, suspensions, among others. For this, we use a method developed by M. Schonbek, known by Fourier Splitting Method. In order to present the method, we first show how it was applied in the context of parabolic conservation laws and the Navier-Stokes equations to obtain decay estimates. Having done this, assuming the existence for solutions of the micropolar fluid system with Dirichlet conditions at infinity and we show the result when the external forces are either null or decay at an appropriate rate. Lastly, through retarded mollifiers and approximate solutions, we guarantee the existence of solutions for the micropolar fluidequations in convenient functional spaces and we prove the desired decay bound.","abstract_has_math":false,"creators":["FREITAS, Lorena Brizza Soares"],"institution":"Universidade Federal de Pernambuco","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["BRAZ E SILVA, Pablo Gustavo Albuquerque"],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-06-14","date_published":"2018-06-14","updated_at":"2026-07-24T01:19:04Z","subjects":["Análise matemática","Equações diferenciais"],"languages":["eng"],"rights":["openAccess","Attribution-NonCommercial-NoDerivs 3.0 Brazil"],"rights_urls":["http://creativecommons.org/licenses/by-nc-nd/3.0/br/"],"identifier_entries":[]},"links":{"outbound_url":"https://repositorio.ufpe.br/handle/123456789/31009","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["BRAZ E SILVA, Pablo Gustavo Albuquerque"]},{"key":"dc:creator","label":"Author","values":["FREITAS, Lorena Brizza Soares"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2019-06-10T23:16:38Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2019-06-10T23:16:38Z"]},{"key":"dc:date.issued","label":"Date","values":["2018-06-14"]},{"key":"dc:publisher","label":"Institution","values":["Universidade Federal de Pernambuco"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Análise matemática","Equações diferenciais"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["openAccess","Attribution-NonCommercial-NoDerivs 3.0 Brazil"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://creativecommons.org/licenses/by-nc-nd/3.0/br/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://repositorio.ufpe.br/handle/123456789/31009"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We obtain decay estimates for solutions of the micropolar fluid equations . Such equations, proposed by A. C. Eringen, generalize the classic model of Navier-Stokes and describe the behavior of fluids with microstructure such as animal blood, liquid crystals, suspensions, among others. For this, we use a method developed by M. Schonbek, known by Fourier Splitting Method. In order to present the method, we first show how it was applied in the context of parabolic conservation laws and the Navier-Stokes equations to obtain decay estimates. Having done this, assuming the existence for solutions of the micropolar fluid system with Dirichlet conditions at infinity and we show the result when the external forces are either null or decay at an appropriate rate. Lastly, through retarded mollifiers and approximate solutions, we guarantee the existence of solutions for the micropolar fluidequations in convenient functional spaces and we prove the desired decay bound."]},{"key":"dc:title","label":"Title","values":["L² decay for weak solutions of the micropolar equations on R³"]}]}],"canonical_facts":{"dc:contributor.advisor":["BRAZ E SILVA, Pablo Gustavo Albuquerque"],"dc:creator":["FREITAS, Lorena Brizza Soares"],"dc:date.accessioned":["2019-06-10T23:16:38Z"],"dc:date.available":["2019-06-10T23:16:38Z"],"dc:date.issued":["2018-06-14"],"dc:description.abstract":["We obtain decay estimates for solutions of the micropolar fluid equations . Such equations, proposed by A. C. Eringen, generalize the classic model of Navier-Stokes and describe the behavior of fluids with microstructure such as animal blood, liquid crystals, suspensions, among others. For this, we use a method developed by M. Schonbek, known by Fourier Splitting Method. In order to present the method, we first show how it was applied in the context of parabolic conservation laws and the Navier-Stokes equations to obtain decay estimates. Having done this, assuming the existence for solutions of the micropolar fluid system with Dirichlet conditions at infinity and we show the result when the external forces are either null or decay at an appropriate rate. Lastly, through retarded mollifiers and approximate solutions, we guarantee the existence of solutions for the micropolar fluidequations in convenient functional spaces and we prove the desired decay bound."],"dc:identifier.uri":["https://repositorio.ufpe.br/handle/123456789/31009"],"dc:language.iso":["eng"],"dc:publisher":["Universidade Federal de Pernambuco"],"dc:rights":["openAccess","Attribution-NonCommercial-NoDerivs 3.0 Brazil"],"dc:rights.uri":["http://creativecommons.org/licenses/by-nc-nd/3.0/br/"],"dc:subject":["Análise matemática","Equações diferenciais"],"dc:title":["L² decay for weak solutions of the micropolar equations on R³"],"dc:type":["doctoralThesis"]},"updated_at":"2026-07-24T01:19:04Z"}