Global controllability of Boussinesq channel flows only through the temperature
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912104596897792 |
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| author | Rissel, Manuel |
| author_facet | Rissel, Manuel |
| contents | We show the global approximate controllability of the Boussinesq system with viscosity and diffusion in a planar periodic channel by using only a temperature control supported in a thin strip. At the walls, a slip boundary condition is chosen for the fluid and the normal derivative of the temperature is assumed to vanish. This contributes a first global controllability result of such type for the Boussinesq system in the presence of non-periodic boundary conditions. We resort to a small-time scaling argument to control the vorticity through a large initial temperature. Moreover, relying on the special choice of the domain, we employ J.-M. Coron's return method in order to steer the temperature without significantly impacting the vorticity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_02200 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global controllability of Boussinesq channel flows only through the temperature Rissel, Manuel Analysis of PDEs Optimization and Control 35Q30, 35Q49, 76B75, 80A19, 93B05, 93C10 We show the global approximate controllability of the Boussinesq system with viscosity and diffusion in a planar periodic channel by using only a temperature control supported in a thin strip. At the walls, a slip boundary condition is chosen for the fluid and the normal derivative of the temperature is assumed to vanish. This contributes a first global controllability result of such type for the Boussinesq system in the presence of non-periodic boundary conditions. We resort to a small-time scaling argument to control the vorticity through a large initial temperature. Moreover, relying on the special choice of the domain, we employ J.-M. Coron's return method in order to steer the temperature without significantly impacting the vorticity. |
| title | Global controllability of Boussinesq channel flows only through the temperature |
| topic | Analysis of PDEs Optimization and Control 35Q30, 35Q49, 76B75, 80A19, 93B05, 93C10 |
| url | https://arxiv.org/abs/2411.02200 |