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.

Bibliography:

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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