Optimal control of the two-dimensional stationary Naviers-Stokes equations with measure valued controls
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Identificadores
URI: http://hdl.handle.net/10902/16179DOI: 10.1137/18M1185582
ISSN: 0363-0129
ISSN: 1095-7138
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2019-04Derechos
© Society for Industrial and Applied Mathematics
Publicado en
SIAM Journal on Control and Optimization, 2019, 57(2), 1328-1354
Editorial
Society for Industrial and Applied Mathematics
Palabras clave
Navier-Stokes equations
Borel measures
Sparsity
First and second order optimality conditions
Stability
Resumen/Abstract
In this paper, we consider an optimal control problem for the two-dimensional stationary Navier-Stokes system. Looking for sparsity, we take Borel measures as controls. We prove the well-posedness of the control problem and derive necessary and sufficient conditions for local optimality of the controls. Finally, under a second order condition, we prove rates of the optimal states with respect to small perturbations in the data of the control problem.
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