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A Boundary Control Problem for Stochastic 2D-Navier–Stokes Equations

Author

Listed:
  • Nikolai Chemetov

    (University of São Paulo)

  • Fernanda Cipriano

    (New University of Lisbon)

Abstract

We study a stochastic velocity tracking problem for the 2D-Navier–Stokes equations perturbed by a multiplicative Gaussian noise. From a physical point of view, the control acts through a boundary injection/suction device with uncertainty, modeled by stochastic non-homogeneous Navier-slip boundary conditions. We show the existence and uniqueness of the solution to the state equation, and prove the existence of an optimal solution to the control problem.

Suggested Citation

  • Nikolai Chemetov & Fernanda Cipriano, 2024. "A Boundary Control Problem for Stochastic 2D-Navier–Stokes Equations," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1847-1879, November.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:2:d:10.1007_s10957-024-02416-3
    DOI: 10.1007/s10957-024-02416-3
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    References listed on IDEAS

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    1. Betül Kalaycı & Ayşe Özmen & Gerhard-Wilhelm Weber, 2020. "Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS," Annals of Operations Research, Springer, vol. 295(1), pages 183-206, December.
    2. Chemetov, Nikolai & Cipriano, Fernanda, 2018. "Optimal control for two-dimensional stochastic second grade fluids," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2710-2749.
    3. Emel Savku, 2023. "A Stochastic Control Approach for Constrained Stochastic Differential Games with Jumps and Regimes," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
    4. Peter Benner & Christoph Trautwein, 2019. "Optimal control problems constrained by the stochastic Navier–Stokes equations with multiplicative Lévy noise," Mathematische Nachrichten, Wiley Blackwell, vol. 292(7), pages 1444-1461, July.
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