Stability analysis of the Navier–Stokes velocity tracking problem with bang-bang controls

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 perturbatio...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2024-05, Vol.201 (2), p.790-824
Main Authors: Domínguez Corella, Alberto, Jork, Nicolai, Nečasová, Šárka, Simon, John Sebastian H.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied mathematics
Approximation
Calculus of Variations and Optimal Control
Optimization
Cost analysis
Dimensional stability
Engineering
Estimates
Fluid flow
Investigations
Mathematics
Mathematics and Statistics
Navier-Stokes equations
Off-on control
Operations Research/Decision Theory
Optimal control
Optimization
Partial differential equations
Sparsity
Stability analysis
Theory of Computation
Tracking problem
Two dimensional analysis
Uncertainty analysis
Velocity
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Summary: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.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02413-6