Cover Image

L² decay for weak solutions of the micropolar equations on R³

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...

Full description

Main Author: FREITAS, Lorena Brizza Soares
Other Authors: BRAZ E SILVA, Pablo Gustavo Albuquerque
Format: doctoralThesis
Language: eng
Published: Universidade Federal de Pernambuco 2019
Subjects:
Análise matemática
Equações diferenciais
Online Access: https://repositorio.ufpe.br/handle/123456789/31009
Tags: Add Tag
No Tags, Be the first to tag this record!
id ir-123456789-31009
recordtype dspace
spelling ir-123456789-310092019-06-11T05:07:13Z L² decay for weak solutions of the micropolar equations on R³ FREITAS, Lorena Brizza Soares BRAZ E SILVA, Pablo Gustavo Albuquerque CRUZ, Felipe Wergete http://lattes.cnpq.br/2302580820419163 http://lattes.cnpq.br/3205167619554233 Análise matemática Equações diferenciais 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. CAPES Obtemos estimativas de decaimento para as soluções das equações para fluidos micropolares. Tais equações, propostas por A. C. Eringen, generalizam o clássico modelo de Navier-Stokes e descrevem o comportamento de fluidos com microestrutura como sangue de animais, cristais líquidos, suspensões, entre outros. Para tal, utilizamos um método desenvolvido por M. Schonbek, conhecido como Método de Decomposição de Fourier. A fim de apresentar o método, primeiramente mostramos como o mesmo foi aplicado no contexto de leis de conservação parabólicas e das equações de Navier-Stokes para obter estimativas de decaimento. Feito isto, assumindo a existência de soluções para o sistema de fluido micropolar com condições de Dirichlet no infinito, obtemos decaimento no caso em que as forças externas do sistema são nulas ou decaem a uma razão apropriada. Por fim, construindo funções suavizantes e soluções aproximadas, garantimos a existência de soluções das equações de fluido micropolar em espaços funcionais convenientes e provamos a estimativa de decaimento desejada. 2019-06-10T23:16:38Z 2019-06-10T23:16:38Z 2018-06-14 doctoralThesis https://repositorio.ufpe.br/handle/123456789/31009 eng openAccess Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ Universidade Federal de Pernambuco UFPE Brasil Programa de Pos Graduacao em Matematica
institution REPOSITORIO UFPE
collection REPOSITORIO UFPE
language eng
topic Análise matemática
Equações diferenciais
spellingShingle Análise matemática
Equações diferenciais
FREITAS, Lorena Brizza Soares
L² decay for weak solutions of the micropolar equations on R³
description 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.
author2 BRAZ E SILVA, Pablo Gustavo Albuquerque
format doctoralThesis
author FREITAS, Lorena Brizza Soares
author_sort FREITAS, Lorena Brizza Soares
title L² decay for weak solutions of the micropolar equations on R³
title_short L² decay for weak solutions of the micropolar equations on R³
title_full L² decay for weak solutions of the micropolar equations on R³
title_fullStr L² decay for weak solutions of the micropolar equations on R³
title_full_unstemmed L² decay for weak solutions of the micropolar equations on R³
title_sort l² decay for weak solutions of the micropolar equations on r³
publisher Universidade Federal de Pernambuco
publishDate 2019
url https://repositorio.ufpe.br/handle/123456789/31009
_version_ 1641987657621831680
score 13.657419

Similar Items