Volume 27, 2021
|Number of page(s)||37|
|Published online||04 June 2021|
Universidad Industrial de Santander, Escuela de Matemáticas,
*** Corresponding author: firstname.lastname@example.org
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.