Optimal control for two-dimensional stochastic second grade fluids

Nikolai Chemetov and Fernanda Cipriano

Stochastic Processes and their Applications, 2018, vol. 128, issue 8, 2710-2749

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.

Keywords: Stochastic second grade fluids; Backward stochastic partial differential equations; Stochastic optimal control; Necessary optimality condition (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:8:p:2710-2749

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DOI: 10.1016/j.spa.2017.09.016

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