Optimal boundary control for the Cahn-Hilliard-Navier-Stokes Equations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910448656318464 |
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| author | Bag, Manika Biswas, Tania Dharmatti, Sheetal |
| author_facet | Bag, Manika Biswas, Tania Dharmatti, Sheetal |
| contents | In this work, we study an optimal boundary control problem for a Cahn - Hilliard -Navier-Stokes (CHNS) system in a two dimensional bounded domain. The CHNS system consists of a Navier-Stokes equation governing the fluid velocity field coupled with a convective Cahn - Hilliard equation for the relative concentration of the fluids. An optimal control problem is formulated as the minimization of a cost functional subject to the controlled CHNS system where the control acts on the boundary of the Navier-Stokes equations. We first prove that there exists an optimal boundary control. Then we establish that the control-to-state operator is Frechet differentiable and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02501 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal boundary control for the Cahn-Hilliard-Navier-Stokes Equations Bag, Manika Biswas, Tania Dharmatti, Sheetal Optimization and Control 49J20, 49J50, 76B99 In this work, we study an optimal boundary control problem for a Cahn - Hilliard -Navier-Stokes (CHNS) system in a two dimensional bounded domain. The CHNS system consists of a Navier-Stokes equation governing the fluid velocity field coupled with a convective Cahn - Hilliard equation for the relative concentration of the fluids. An optimal control problem is formulated as the minimization of a cost functional subject to the controlled CHNS system where the control acts on the boundary of the Navier-Stokes equations. We first prove that there exists an optimal boundary control. Then we establish that the control-to-state operator is Frechet differentiable and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint system. |
| title | Optimal boundary control for the Cahn-Hilliard-Navier-Stokes Equations |
| topic | Optimization and Control 49J20, 49J50, 76B99 |
| url | https://arxiv.org/abs/2305.02501 |