Optimal distributed control of a 2D simplified Ericksen-Leslie system for the nematic liquid crystal flows

We study the initial boundary value problem of a simplified Ericksen-Leslie system modeling the incompressible nematic liquid crystal flows in two dimensions of space, where the equations of the velocity field are characterized by a time-dependent external force g(t) and a no-slip boundary condition, and the equations for the molecular orientation are subjected to a time-dependent Dirichlet boundary condition h(t). Based on the recently addressed well-posedness and regularity results of the system, we present a rigorous proof to show the existence of optimal distributed controls, the control-to-state operator is Frechet differentiable and first-order necessary optimality conditions for an associated optimal control problem. (C) 2019 Elsevier Ltd. All rights reserved.