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Session S17 - Stochastic Systems: Analysis, Numerics and Applications

Tuesday, July 13, 15:20 ~ 15:55 UTC-3

Optimal control for two-dimensional stochastic second grade fluids

Nikolai V. Chemetov

University of São Paulo, Brasil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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.

Also we will discuss the uniqueness result.


Chemetov N.V., Cipriano F., Optimal control for two-dimensional stochastic second grade fluids. Stochastic Processes and their Applications, 128, n. 8, 2710-2749 (2018).

Chemetov N.V., Cipriano F., Well-posedness of stochastic second grade fluids, J. Mathematical Analysis and Applications, 454, n.2, 585-616 (2017).

Chemetov N.V., Cipriano F., Injection-Suction Control for Two-Dimensional Navier--Stokes Equations with Slippage, SIAM Journal on Control and Optimization, 56, n. 2, 1253-1281 (2018).

Joint work with F. Cipriano (Universidade Nova de Lisboa, Portugal).

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