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Exact controllability of Galerkin's approximations of micropolar fluids


Authors: F. D. Araruna, F. W. Chaves-Silva and M. A. Rojas-Medar
Journal: Proc. Amer. Math. Soc. 138 (2010), 1361-1370
MSC (2000): Primary 35Q35, 93B05; Secondary 65M60
Published electronically: November 2, 2009
MathSciNet review: 2578528
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the nonlinear model describing micropolar fluid in a bounded smooth region of $ \mathbb{R}^{N} (N=2,3)$ with distributed controls supported in small subset of this domain. Under suitable assumptions on the Galerkin basis, we introduce Galerkin's approximations for the controllable micropolar fluid system. By using the Hilbert Uniqueness Method in combination with a fixed point argument, we prove the exact controllability result for this finite-dimensional system.


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Additional Information

F. D. Araruna
Affiliation: Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, João Pessoa, PB, Brazil
Email: fagner@mat.ufpb.br

F. W. Chaves-Silva
Affiliation: Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, João Pessoa, PB, Brazil
Email: felipewallison@hotmail.com

M. A. Rojas-Medar
Affiliation: Departamento de Ciencias Básicas, Universidad del Bío-Bío, Campus Fernando May, Casilla 447, Chillán, Chile
Email: marko@ueubiobio.cl

DOI: https://doi.org/10.1090/S0002-9939-09-10154-5
Keywords: Micropolar fluids, controllability, Galerkin approximations
Received by editor(s): March 30, 2009
Received by editor(s) in revised form: July 1, 2009, July 14, 2009, and July 29, 2009
Published electronically: November 2, 2009
Additional Notes: The first author was supported by CNPq-Brazil and FAPESQ-PB-Brazil
The second author was supported by CAPES-Brazil.
The third author was partially supported by Fondecyt-Chile, Grant 1080628 and MTM2006-07932, Spain.
Communicated by: Walter Craig
Article copyright: © Copyright 2009 American Mathematical Society