Optimal control for the coupled chemotaxis-fluid models in two space dimensions

Abstract

<p style='text-indent:20px;'>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.</p>