Uniform local null control of the Leray-$α$ model
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911774089936896 |
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| author | Araruna, Fágner D. Fernández-Cara, Enrique Souza, Diego A. |
| author_facet | Araruna, Fágner D. Fernández-Cara, Enrique Souza, Diego A. |
| contents | This paper deals with the distributed and boundary controllability of the so called Leray-$α$ model. This is a regularized variant of the Navier-Stokes system ($α$ is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray-$α$ equations are locally null controllable, with controls bounded independently of $α$. We also prove that, if the initial data are sufficiently small, the controls converge as $α\to 0^+$ to a null control of the Navier-Stokes equations. We also discuss some other related questions, such as global null controllability, local and global exact controllability to the trajectories, etc. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform local null control of the Leray-$α$ model Araruna, Fágner D. Fernández-Cara, Enrique Souza, Diego A. Optimization and Control 93B05, 35Q35, 35G25, 93B07 This paper deals with the distributed and boundary controllability of the so called Leray-$α$ model. This is a regularized variant of the Navier-Stokes system ($α$ is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray-$α$ equations are locally null controllable, with controls bounded independently of $α$. We also prove that, if the initial data are sufficiently small, the controls converge as $α\to 0^+$ to a null control of the Navier-Stokes equations. We also discuss some other related questions, such as global null controllability, local and global exact controllability to the trajectories, etc. |
| title | Uniform local null control of the Leray-$α$ model |
| topic | Optimization and Control 93B05, 35Q35, 35G25, 93B07 |
| url | https://arxiv.org/abs/2402.06307 |