An Optimal Control Problem for a Generalized Bioconvective Flow

In this work, we consider an optimal control problem for a generalized model for bioconvective flows, which are convection flows caused by the differences in the concentration of upward swimming microorganisms in a fluid. We firstly study the existence of weak solutions for the mathematical fluid model; then we prove the existence of optimal controls and obtain the corresponding first order optimality conditions by using the Dubovitskii-Milyutin formalism.