An Optimal Control Problem for the Navier--Stokes Equations with Point Sources
Optimization and Control
2022-08-19 v2
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.
Cite
@article{arxiv.2112.15061,
title = {An Optimal Control Problem for the Navier--Stokes Equations with Point Sources},
author = {Francisco Fuica and Felipe Lepe and Enrique Otarola and Daniel Quero},
journal= {arXiv preprint arXiv:2112.15061},
year = {2022}
}