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An Optimal Control Problem for the Navier–Stokes Equations with Point Sources

Author

Listed:
  • Francisco Fuica

    (Universidad Técnica Federico Santa María)

  • Felipe Lepe

    (Universidad del Bío Bío)

  • Enrique Otárola

    (Universidad Técnica Federico Santa María)

  • Daniel Quero

    (Universidad Técnica Federico Santa María)

Abstract

We analyze, in two dimensions, an optimal control problem for the Navier–Stokes equations where the control variable corresponds to the amplitude of forces modeled as point sources; control constraints are also considered. This particular setting leads to solutions to the state equation exhibiting reduced regularity properties. We operate under the framework of Muckenhoupt weights, Muckenhoupt-weighted Sobolev spaces, and the corresponding weighted norm inequalities and derive the existence of optimal solutions and first- and, necessary and sufficient, second-order optimality conditions.

Suggested Citation

  • Francisco Fuica & Felipe Lepe & Enrique Otárola & Daniel Quero, 2023. "An Optimal Control Problem for the Navier–Stokes Equations with Point Sources," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 590-616, February.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:2:d:10.1007_s10957-022-02148-2
    DOI: 10.1007/s10957-022-02148-2
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    References listed on IDEAS

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    1. Georg Stadler, 2009. "Elliptic optimal control problems with L 1 -control cost and applications for the placement of control devices," Computational Optimization and Applications, Springer, vol. 44(2), pages 159-181, November.
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