Open AccessOptimal control for the coupled chemotaxis-fluid models in two space dimensions
Author(s) -
Yunfei Yuan,
Changchun Liu
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021085
Subject(s) - lagrange multiplier , uniqueness , chemotaxis , space (punctuation) , mathematics , multiplier (economics) , optimal control , mathematical optimization , mathematical analysis , computer science , economics , biochemistry , chemistry , receptor , macroeconomics , operating system
This paper deals with a distributed optimal control problem to the coupled chemotaxis-fluid models. We first explore the global-in-time existence and uniqueness of a strong solution. Then, we define the cost functional and establish the existence of Lagrange multipliers. Finally, we derive some extra regularity for the Lagrange multiplier.