Optimal cost for the null controllability of the Stokes system with controls having n-1 components and applications

2025/12/04 by Felipe W. Chaves-Silva, Chaves-Silva, Felipe W., Marcos G. Ferreira-Silva +3
Computer Science · Engineering · Mathematics · #35K40 #35Q30 #49J20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2512.04721

openalex publication_date 2025/12/04 · openalex created_date 2025/12/06 · openalex updated_date 2026/07/28

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.

Citations

• The Kalman rank condition and the optimal cost for the null-controllability of coupled Stokes systems
• Observability inequalities on measurable sets for the Stokes system and applications
• Local null controllability of the three-dimensional Navier-Stokes system\n with a distributed control having two vanishing components

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• The Kalman rank condition and the optimal cost for the null-controllability of coupled Stokes systems
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