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Optimal control for two-dimensional stochastic second grade fluids

Author

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  • Chemetov, Nikolai
  • Cipriano, Fernanda

Abstract

This article deals with a stochastic control problem for certain fluids of non-Newtonian type. More precisely, the state equation is given by the two-dimensional stochastic second grade fluids perturbed by a multiplicative white noise. The control acts through an external stochastic force and we search for a control that minimizes a cost functional. We show that the Gâteaux derivative of the control to state map is a stochastic process being the unique solution of the stochastic linearized state equation. The well-posedness of the corresponding stochastic backward adjoint equation is also established, allowing to derive the first order optimality condition.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:8:p:2710-2749
    DOI: 10.1016/j.spa.2017.09.016
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    References listed on IDEAS

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    1. Cipriano, Fernanda & Torrecilla, Iván, 2015. "Inviscid limit for 2D stochastic Navier–Stokes equations," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2405-2426.
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    Cited by:

    1. Evgenii S. Baranovskii & Mikhail A. Artemov, 2021. "Optimal Control for a Nonlocal Model of Non-Newtonian Fluid Flows," Mathematics, MDPI, vol. 9(3), pages 1-16, January.

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