A Boundary Control Problem for Micropolar Fluids

Exequiel Mallea-Zepeda (), Elva Ortega-Torres () and Élder J. Villamizar-Roa ()
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Exequiel Mallea-Zepeda: Universidad Católica del Norte
Elva Ortega-Torres: Universidad Católica del Norte
Élder J. Villamizar-Roa: Universidad Industrial de Santander

Journal of Optimization Theory and Applications, 2016, vol. 169, issue 2, No 1, 349-369

Abstract: Abstract An optimal boundary control problem for the micropolar fluid equations in 3D bounded domains, with mixed boundary conditions, is analyzed. By considering boundary controls for the velocity vector and the angular velocity of rotation of particles, the existence of optimal solutions is proved. The analyzed optimal boundary control problem includes the minimization of a Lebesgue norm between the velocities and some desired fields, as well as the resistance in the fluid due to the viscous friction. By using the Theorem of Lagrange multipliers, an optimality system is derived. A second-order sufficient condition is also given.

Keywords: Optimal boundary control; Micropolar fluids; Optimality conditions; 49J20; 76D55; 35Q30 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-016-0925-y

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