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

Publication date: February 2020Source: Nonlinear Analysis: Real World Applications, Volume 51Author(s): Qiao LiuAbstractWe 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.

Source: Nonlinear Analysis: Real World Applications - August 29, 2019 Category: Research Source Type: research