On the uniqueness of the optimal control for 2-dimensional second grade fluids
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929482035625984 |
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| author | Almeida, Adilson Chemetov, Nikolai V. Cipriano, Fernanda |
| author_facet | Almeida, Adilson Chemetov, Nikolai V. Cipriano, Fernanda |
| contents | We study an optimal control problem with a quadratic cost functional for non-Newtonian fluids of differential type.
More precisely, we consider the system governing the evolution of a second grade fluid filling a two-dimensional bounded domain, supplemented with a Navier slip boundary condition, and under certain assumptions on the size of the initial data and parameters of the model, we prove the second-order sufficient optimality conditions.
Furthermore, we establish a global uniqueness result for the solutions of the first-order optimality system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00537 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the uniqueness of the optimal control for 2-dimensional second grade fluids Almeida, Adilson Chemetov, Nikolai V. Cipriano, Fernanda Analysis of PDEs Optimization and Control 35R60, 49K20, 60G15, 60H15, 76D55 We study an optimal control problem with a quadratic cost functional for non-Newtonian fluids of differential type. More precisely, we consider the system governing the evolution of a second grade fluid filling a two-dimensional bounded domain, supplemented with a Navier slip boundary condition, and under certain assumptions on the size of the initial data and parameters of the model, we prove the second-order sufficient optimality conditions. Furthermore, we establish a global uniqueness result for the solutions of the first-order optimality system. |
| title | On the uniqueness of the optimal control for 2-dimensional second grade fluids |
| topic | Analysis of PDEs Optimization and Control 35R60, 49K20, 60G15, 60H15, 76D55 |
| url | https://arxiv.org/abs/2409.00537 |