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Citation:

Chemetov, Nikolai, and Fernanda Cipriano. "Optimal control for two-dimensional stochastic second grade fluids." STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 128 (2018): 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 Gateaux 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. (C) 2017 Elsevier B.V. All rights reserved.}

Notes:

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