Optimal control for two-dimensional stochastic second grade fluids

Nikolai Chemetov; Fernanda Cipriano

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arXiv · 1706.05526

Optimal control for two-dimensional stochastic second grade fluids

Nikolai Chemetov·Fernanda Cipriano

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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 G\^ateaux 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.

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Nikolai Chemetov, Fernanda Cipriano. 2017-06-17. Optimal control for two-dimensional stochastic second grade fluids. https://arxiv.org/abs/1706.05526

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