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

Dominguez Corella A, Jork N, Necasova S, Simon J (2024)

Publication Status: In review

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2024

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.

Authors with CRIS profile

Alberto Dominguez Corella Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Academy of Sciences of the Czech Republic (ASCR) / Akademie věd České republiky (AVČR) CZ Czech Republic (CZ)

How to cite

APA:

Dominguez Corella, A., Jork, N., Necasova, S., & Simon, J. (2024). Stability analysis of the Navier-Stokes velocity tracking problem with bang-bang controls. (Unpublished, In review).

MLA:

Dominguez Corella, Alberto, et al. Stability analysis of the Navier-Stokes velocity tracking problem with bang-bang controls. Unpublished, In review. 2024.

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