{"ID":2832960,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.04721","arxiv_id":"2512.04721","title":"Optimal cost for the null controllability of the Stokes system with controls having $n-1$ components and applications","abstract":"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.","short_abstract":"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 controll...","url_abs":"https://arxiv.org/abs/2512.04721","url_pdf":"https://arxiv.org/pdf/2512.04721v3","authors":"[\"Felipe W. Chaves-Silva\",\"Marcos G. Ferreira-Silva\",\"Diego A. Souza\"]","published":"2025-12-04T12:05:52Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.OC\"]","methods":"[]","has_code":false}