Título: On the optimal control of non-Newtonian fluids.
Data: 12/07/2023
Horário: 12:00h
Local: C-116
Palestrante: Fernanda Cipriano (Universidade Nova de Lisboa)
Resumo:
We discuss the optimal control problems of flows governed by the incompressible deterministic and stochastic third grade fluid equations with Navier-slip boundary conditions.
After recalling the results on the well-posedness of the state equations, we study the existence and the uniqueness of solution to the linearized state and adjoint equations. Furthermore, we present a stability result for the state, and show that the solution of the linearized equation coincides with the Gâteaux derivative of the control-to-state mapping. Next, we prove the existence of an optimal solution and establish the first order optimality conditions.
In the deterministic case, an uniqueness result of the coupled system constituted by the state equation, the adjoint equation and the first order optimality condition is established, under sufficiently large intensity of the cost.
This is a joint work with Y. Tahraoui.
Bibliography:
[1] A. Almeida, N. Chemetov and F. Cipriano, Uniqueness for optimal control problems of two-dimensional second grade fluids. EJDE, Vol. 2022, No. 22, 1-12 (2022)
[2] N. Chemetov, F. Cipriano, Optimal control for two-dimensional stochastic second grade fluids. Stochastic Processes Appl., 128, Issue 8, 2710-2749 (2018)
[3] F. Cipriano, P. Didier, S. Guerra, Well-posedness of stochastic third grade fluid equation. J. Diff. Eq., 285, 496-535 (2021)
[4] Y. Tahraoui and F. Cipriano, Optimal control of two dimensional third grade fluids. J. Math. Anal. Appl., 523, 127032, (2023)
[5] Y. Tahraoui and F. Cipriano, Local strong solutions to the stochastic third grade fluid equations with Navier Boundary conditions,
https://doi.org/10.48550/
