Local exact controllability to the trajectories of the liquid crystal flow and global null controllability of the liquid crystal flow with an external field

<p dir="ltr">This dissertation encompasses my research work during my Ph.D. career, focusing on the controllability properties of liquid crystal flow. I have achieved two main results, which are as follows: Firstly, I have established the local exact controllability to the trajectory of the simplified Ericksen-Leslie model and its Ginzburg-Landau approximation. Secondly, I have successfully proven the global null controllability of the simplified Ericksen-Leslie model with Lions boundary condition for u and Neumann boundary condition for d, with the aid of a globally defined magnetic field which is independent of the spatial variable x. </p>