Volume 27, 2021
|Number of page(s)||37|
|Published online||04 June 2021|
An optimal control problem related to a 3D-chemotaxis-Navier-Stokes model*,**
Universidad Industrial de Santander, Escuela de Matemáticas,
*** Corresponding author: email@example.com
Accepted: 20 May 2021
In this paper, we study an optimal control problem associated to a 3D-chemotaxis-Navier-Stokes model. First we prove the existence of global weak solutions of the state equations with a linear reaction term on the chemical concentration equation, and an external source on the velocity equation, both acting as controls on the system. Second, we establish a regularity criterion to get global-in-time strong solutions. Finally, we prove the existence of an optimal solution, and we establish a first-order optimality condition.
Mathematics Subject Classification: 35Q35 / 35K51 / 49J20 / 49K20 / 76D55
Key words: Optimal control problem / chemotaxis-fluid model / optimality conditions
J. López-Ríos was supported by MINCIENCIAS, convocatoria 848-2019, posdoc project Fondo Nacional de Financiamiento Para la Ciencia, la Tecnología y la Innovación “Francisco José de Caldas”, number 80740-067-2020.
© The authors. Published by EDP Sciences, SMAI 2021
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