| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 58 | |
| Number of page(s) | 37 | |
| DOI | https://doi.org/10.1051/cocv/2021055 | |
| Published online | 04 June 2021 | |
An optimal control problem related to a 3D-chemotaxis-Navier-Stokes model*,**
Universidad Industrial de Santander, Escuela de Matemáticas,
A.A. 678,
Bucaramanga, Colombia.
*** Corresponding author: jvillami@uis.edu.co
Received:
26
March
2020
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
© The authors. Published by EDP Sciences, SMAI 2021
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