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

Francisco Fuica (), Felipe Lepe (), Enrique Otárola () and Daniel Quero ()
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Francisco Fuica: Universidad Técnica Federico Santa María
Felipe Lepe: Universidad del Bío Bío
Enrique Otárola: Universidad Técnica Federico Santa María
Daniel Quero: Universidad Técnica Federico Santa María

Journal of Optimization Theory and Applications, 2023, vol. 196, issue 2, No 9, 590-616

Abstract: Abstract 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.

Keywords: Optimal control problems; Navier–Stokes equations; Dirac measures; Muckenhoupt weights; First- and second-order optimality conditions; 35Q30; 49J20; 49K20 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-022-02148-2

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