0585939 - MÚ 2025 RIV DE eng J - Journal Article
Corella, A. D. - Jork, N. - Nečasová, Šárka - Simon, J. S. H.
Stability analysis of the Navier–Stokes velocity tracking problem with bang-bang controls.
Journal of Optimization Theory and Applications. Roč. 201, č. 2 (2024), s. 790-824. ISSN 0022-3239. E-ISSN 1573-2878
R&D Projects: GA ČR(CZ) GC22-08633J
Grant - others:AV ČR(CZ) AP2101
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985840
Keywords : Navier-Stokes equations * optimality conditions * stability analysis * Tikhonov regularization
OECD category: Pure mathematics
Impact factor: 1.6, year: 2023
Method of publishing: Limited access
https://doi.org/10.1007/s10957-024-02413-6

This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier-Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence bang-bang solutions can be expected. We investigate perturbations that account for uncertainty in the tracking data and the initial condition of the state, and analyze the convergence rate of solutions when the original problem is regularized by the Tikhonov term. The stability analysis relies on the Hölder subregularity of the optimality mapping, which stems from the necessary conditions of the problem.
Permanent Link: https://hdl.handle.net/11104/0353573