Strong well-posedness and dynamics of a nematic liquid crystal-colloidal interaction model

This paper investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a colloidal particle. It is shown that this problem is locally strongly well-posed, and that it also admits a unique global strong solution for initial data close to constant equilibria. The proof relies on the property of maximal regularity of the corresponding linearized problem. In particular, for the global well-posedness, a splitting of the director part in mean value zero and average part is employed.