An Optimal Control Problem for the Navier--Stokes Equations with Point Sources

We analyze, in two dimensions, an optimal control problem for the Navier--Stokes equations where the control variable corresponds to the amplitude of forces modeled as point sources; control constraints are also considered. This particular setting leads to solutions to the state equation exhibiting...

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Bibliographic Details
Main Authors Fuica, Francisco, Lepe, Felipe, Otarola, Enrique, Quero, Daniel
Format Journal Article
LanguageEnglish
Published 30.12.2021
Subjects
Mathematics - Optimization and Control
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Summary:We analyze, in two dimensions, an optimal control problem for the Navier--Stokes equations where the control variable corresponds to the amplitude of forces modeled as point sources; control constraints are also considered. This particular setting leads to solutions to the state equation exhibiting reduced regularity properties. We operate under the framework of Muckenhoupt weights, Muckenhoupt-weighted Sobolev spaces, and the corresponding weighted norm inequalities and derive the existence of optimal solutions and first and, necessary and sufficient, second order optimality conditions.
DOI:10.48550/arxiv.2112.15061