Exact controllability of Galerkin's approximations of micropolar fluids

F. D. Araruna; F. W. Chaves-Silva; M. A. Rojas-Medar

doi:10.1090/S0002-9939-09-10154-5

Exact controllability of Galerkin's approximations of micropolar fluids

F. D. Araruna
, F. W. Chaves-Silva
, M. A. Rojas-Medar

Universidade Federal da Paraíba
Universidad del Bío-Bío

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We consider the nonlinear model describing micropolar fluid in a bounded smooth region of 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 finitedimensional system.

Original language	English
Pages (from-to)	1361-1370
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	138
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-09-10154-5
State	Published - Apr 2010
Externally published	Yes

Keywords

Controllability
Galerkin approximations
Micropolar fluids

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Cite this

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abstract = "We consider the nonlinear model describing micropolar fluid in a bounded smooth region of ℝN(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 finitedimensional system.",

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N2 - We consider the nonlinear model describing micropolar fluid in a bounded smooth region of ℝN(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 finitedimensional system.

AB - We consider the nonlinear model describing micropolar fluid in a bounded smooth region of ℝN(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 finitedimensional system.

KW - Controllability

KW - Galerkin approximations

KW - Micropolar fluids

UR - https://www.scopus.com/pages/publications/77951440041

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JO - Proceedings of the American Mathematical Society

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ER -

Exact controllability of Galerkin's approximations of micropolar fluids

Abstract

Keywords

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