Optimal control problem associated with three-dimensional critical convective Brinkman-Forchheimer equations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911390413881344 |
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| author | Kinra, Kush Cipriano, Fernanda |
| author_facet | Kinra, Kush Cipriano, Fernanda |
| contents | In this article, we are concerned about the velocity tracking optimal control problem for 3D critical convective Brinkman-Forchheimer equations defined on a simply connected bounded domain $\mathbb{D}\subset\mathbb{R}^3$ with $\mathrm{C}^2$-boundary $\partial\mathbb{D}$. The control is introduced through an external force. The objective is to optimally minimize a velocity tracking cost functional, for which the velocity vector field is oriented towards a target velocity. Most importantly, we are concerned about the first-order necessary optimality conditions for above-mentioned optimal control problem which is the main challenging task of this article. To overcome the difficulties related to the differentiability of the control-to-state mapping, consequence of the lack of regularity of the state variable on bounded domains, we first establish some intermediate optimality conditions and then pass to the limit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_15242 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal control problem associated with three-dimensional critical convective Brinkman-Forchheimer equations Kinra, Kush Cipriano, Fernanda Optimization and Control 49J20, 35Q35, 49K20, 76D55 In this article, we are concerned about the velocity tracking optimal control problem for 3D critical convective Brinkman-Forchheimer equations defined on a simply connected bounded domain $\mathbb{D}\subset\mathbb{R}^3$ with $\mathrm{C}^2$-boundary $\partial\mathbb{D}$. The control is introduced through an external force. The objective is to optimally minimize a velocity tracking cost functional, for which the velocity vector field is oriented towards a target velocity. Most importantly, we are concerned about the first-order necessary optimality conditions for above-mentioned optimal control problem which is the main challenging task of this article. To overcome the difficulties related to the differentiability of the control-to-state mapping, consequence of the lack of regularity of the state variable on bounded domains, we first establish some intermediate optimality conditions and then pass to the limit. |
| title | Optimal control problem associated with three-dimensional critical convective Brinkman-Forchheimer equations |
| topic | Optimization and Control 49J20, 35Q35, 49K20, 76D55 |
| url | https://arxiv.org/abs/2601.15242 |