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:arXiv.org 2024-02
Main Authors: Alberto Domínguez Corella, Jork, Nicolai, Nečasová, Šarká, Simon, John Sebastian H
Format: Article
Language:English
Subjects:
Cost analysis
Dimensional stability
Fluid flow
Navier-Stokes equations
Off-on control
Optimal control
Optimization
Stability analysis
Tracking problem
Two dimensional analysis
Uncertainty analysis
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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 H\"older subregularity of the optimality mapping, which stems from the necessary conditions of the problem.
ISSN:2331-8422