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.
Keywords: Optimal control problem, chemotaxis-fluid model, optimality conditions
@article{COCV_2021__27_1_A60_0,
author = {L\'opez-R{\'\i}os, J. and Villamizar-Roa, \'Elder J.},
title = {An optimal control problem related to a {3D-chemotaxis-Navier-Stokes} model},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021055},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021055/}
}
TY - JOUR AU - López-Ríos, J. AU - Villamizar-Roa, Élder J. TI - An optimal control problem related to a 3D-chemotaxis-Navier-Stokes model JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021055/ DO - 10.1051/cocv/2021055 LA - en ID - COCV_2021__27_1_A60_0 ER -
%0 Journal Article %A López-Ríos, J. %A Villamizar-Roa, Élder J. %T An optimal control problem related to a 3D-chemotaxis-Navier-Stokes model %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021055/ %R 10.1051/cocv/2021055 %G en %F COCV_2021__27_1_A60_0
López-Ríos, J.; Villamizar-Roa, Élder J. An optimal control problem related to a 3D-chemotaxis-Navier-Stokes model. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 58. doi: 10.1051/cocv/2021055
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Cité par Sources :
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.
E.J. Villamizar-Roa was supported by Vicerrectoría de Investigación y Extensión of Universidad Industrial de Santander, Project “Estudio teórico de problemas de quimiotaxis-haptotaxis en dominios no acotados”, code C-2020-05.
