Abstract
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 Fréchet differentiable and first-order necessary optimality conditions for an associated optimal control problem.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
