Optimal boundary control of a simplified Ericksen-Leslie system for nematic liquid crystal flows in \(2D\) (Q524315)

This paper deals with the optimal boundary control problem for a hydrodynamic system for incompressible liquid crystal flows of nematic type in a bounded domain with a smooth boundary; some stability estimates for global strong solutions in higher-order Sobolev norms when the spatial dimension is two are established. The existence of an optimal boundary control over a suitable set is proved. It is shown that the control-to-state operator is Fréchet differentiable between appropriate Banach spaces, and the first-order necessary optimality condition is derived.