Optimal control of Newtonian fluids in a stochastic environment
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913488191881216 |
|---|---|
| author | Chemetov, Nikolai Cipriano, Fernanda |
| author_facet | Chemetov, Nikolai Cipriano, Fernanda |
| contents | 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 non-homogeneous 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 Gâteaux 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00479 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal control of Newtonian fluids in a stochastic environment Chemetov, Nikolai Cipriano, Fernanda Probability Analysis of PDEs Optimization and Control 60H15, 6D55, 93E20, 49K45 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 non-homogeneous 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 Gâteaux 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. |
| title | Optimal control of Newtonian fluids in a stochastic environment |
| topic | Probability Analysis of PDEs Optimization and Control 60H15, 6D55, 93E20, 49K45 |
| url | https://arxiv.org/abs/2409.00479 |