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 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.

Grantor dc:publisher

Universidade Federal de Pernambuco

Year dc:date.issued

2018

Author dc:creator

• FREITAS, Lorena Brizza Soares

Advisor dc:contributor.advisor

• BRAZ E SILVA, Pablo Gustavo Albuquerque

• Análise matemática
• Equações diferenciais

Statement dc:rights

• openAccess
• Attribution-NonCommercial-NoDerivs 3.0 Brazil

Licence dc:rights.uri

• http://creativecommons.org/licenses/by-nc-nd/3.0/br/

Language dc:language.iso

eng

Repository record dc:identifier.uri

https://repositorio.ufpe.br/handle/123456789/31009

OAI identifier oai:identifier

oai:repositorio.ufpe.br:123456789/31009