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

Alberto Domínguez Corella (), Nicolai Jork (), Šárka Nečasová () and John Sebastian H. Simon ()
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Alberto Domínguez Corella: Friedrich-Alexander-Universität Erlangen-Nürnberg
Nicolai Jork: Vienna University of Technology
Šárka Nečasová: Czech Academy of Sciences
John Sebastian H. Simon: Austrian Academy of Sciences

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 2, No 11, 790-824

Abstract: Abstract 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.

Keywords: Navier–Stokes equations; Stability analysis; Optimality conditions; Tikhonov regularization; 49K20; 49K30; 49K40; 76D05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02413-6

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