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arXiv · 2112.15061

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

Francisco Fuica·Felipe Lepe·Enrique Otarola·Daniel Quero
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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.

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Francisco Fuica, Felipe Lepe, Enrique Otarola, Daniel Quero. 2021-12-30. An Optimal Control Problem for the Navier--Stokes Equations with Point Sources. https://arxiv.org/abs/2112.15061

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