Optimal cost for the null controllability of the Stokes system with controls having $n-1$ components and applications
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| Format: | Preprint |
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2025
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| author | Chaves-Silva, Felipe W. Ferreira-Silva, Marcos G. Souza, Diego A. |
| author_facet | Chaves-Silva, Felipe W. Ferreira-Silva, Marcos G. Souza, Diego A. |
| contents | In this work, we investigate the optimal cost of null controllability for the $n$-dimensional Stokes system when the control acts on $n-1$ scalar components. We establish a novel spectral estimate for low frequencies of the Stokes operator, involving solely $n-1$ components, and use it to show that the cost of controllability with controls having $n-1$ components remains of the same order in time as in the case of controls with $n$ components, namely $O(e^{C/T})$, i.e. the cost of null controllability is not affected by the absence of one component of the control. We also give several applications of our results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_04721 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal cost for the null controllability of the Stokes system with controls having $n-1$ components and applications Chaves-Silva, Felipe W. Ferreira-Silva, Marcos G. Souza, Diego A. Analysis of PDEs Optimization and Control 35K40, 35Q30, 49J20 In this work, we investigate the optimal cost of null controllability for the $n$-dimensional Stokes system when the control acts on $n-1$ scalar components. We establish a novel spectral estimate for low frequencies of the Stokes operator, involving solely $n-1$ components, and use it to show that the cost of controllability with controls having $n-1$ components remains of the same order in time as in the case of controls with $n$ components, namely $O(e^{C/T})$, i.e. the cost of null controllability is not affected by the absence of one component of the control. We also give several applications of our results. |
| title | Optimal cost for the null controllability of the Stokes system with controls having $n-1$ components and applications |
| topic | Analysis of PDEs Optimization and Control 35K40, 35Q30, 49J20 |
| url | https://arxiv.org/abs/2512.04721 |