| Full text | |
| Author(s): |
Chemetov, Nikolai, V
;
Cipriano, Fernanda
Total Authors: 2
|
| Document type: | Journal article |
| Source: | SIAM JOURNAL ON MATHEMATICAL ANALYSIS; v. 57, n. 1, p. 40-pg., 2025-01-01. |
| Abstract | |
We consider a velocity tracking problem for stochastic Navier-Stokes equations in a 2D-bounded domain. The control acts on the boundary through an injection-suction device with uncertainty, which acts in accordance with the nonhomogeneous Navier-slip boundary conditions. After establishing a suitable stability result for the solution of the stochastic state equation, we prove the well-posedness of the stochastic linearized state equation and show that the Ga<^>\teaux derivative of the control-to-state mapping corresponds to the unique solution of the linearized equation. Next, we study the stochastic backward adjoint equation and establish a duality relation between the solutions of the forward linearized equation and the backward adjoint equation. Finally, we derive the first-order optimality conditions. (AU) | |
| FAPESP's process: | 23/05271-4 - Optimal boundary control problem for stochastic Navier-Stokes equations |
| Grantee: | Nikolai Vasilievich Chemetov |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 21/03758-8 - Mathematical problems in fluid dynamics |
| Grantee: | Nikolai Vasilievich Chemetov |
| Support Opportunities: | Regular Research Grants |