First- and second-order optimality conditions for the control of infinite horizon Navier-Stokes equations

First and second order optimality conditions for the control of in nite horizon Navier-Stokes equations

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URI: https://hdl.handle.net/10902/38376
ISSN: 0233-1934
ISSN: 1029-4945
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Autoría
Casas Rentería, EduardoAutoridad Unican; Kunisch, Karl
Fecha
2024-05-14
Derechos
This is an Accepted Manuscript version of the following article, accepted for publication in Optimization. Casas, E., Kunisch, K. 2025. First- and second-order optimality conditions for the control of infinite horizon Navier–Stokes equations. Optimization, 74(13), 3037-3080. It is deposited under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
Publicado en
Optimization, 2025, 74(13), 3037-3080
Editorial
Taylor and Francis Ltd.
Disponible después de
2026-01-01
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Palabras clave
In nite horizon optimal control
Navier Stokes equations
Second order optimality conditions
Sparsity promoting cost functional
Nonsmooth optimization
Euclidean norm constraints
Resumen/Abstract
First and second-order optimality conditions for optimal control problems over the infinite time horizon subject to the Navier-Stokes equations are derived. The cost functional enhances temporal sparsity of the controls, which implies that the optimal controls shut down in finite time. The problem formulation also includes explicit constraints on the control which may be non-smooth and non-affine.
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This is an Accepted Manuscript version of the following article, accepted for publication in Optimization. Casas, E., Kunisch, K. 2025. First- and second-order optimality conditions for the control of infinite horizon Navier–Stokes equations. Optimization, 74(13), 3037-3080. It is deposited under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.Excepto si se señala otra cosa, la licencia del ítem se describe como This is an Accepted Manuscript version of the following article, accepted for publication in Optimization. Casas, E., Kunisch, K. 2025. First- and second-order optimality conditions for the control of infinite horizon Navier–Stokes equations. Optimization, 74(13), 3037-3080. It is deposited under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.