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A Boundary Control Problem for Micropolar Fluids

Author

Listed:
  • Exequiel Mallea-Zepeda

    (Universidad Católica del Norte)

  • Elva Ortega-Torres

    (Universidad Católica del Norte)

  • Élder J. Villamizar-Roa

    (Universidad Industrial de Santander)

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.

Suggested Citation

  • Exequiel Mallea-Zepeda & Elva Ortega-Torres & Élder J. Villamizar-Roa, 2016. "A Boundary Control Problem for Micropolar Fluids," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 349-369, May.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:2:d:10.1007_s10957-016-0925-y
    DOI: 10.1007/s10957-016-0925-y
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    Cited by:

    1. Gennadii Alekseev, 2023. "Analysis of Control Problems for Stationary Magnetohydrodynamics Equations under the Mixed Boundary Conditions for a Magnetic Field," Mathematics, MDPI, vol. 11(12), pages 1-29, June.

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