Regularity and time-periodicity for a nematic liquid crystal model

In this paper two main results are obtained for a nematic liquid crystal model with time-dependent boundary Dirichlet data for the orientation of the crystal molecules. First, the initial-boundary problem is considered, obtaining the existence of global in time (up to infinity time) weak solution, the existence of global regular solution for viscosity coefficient big enough, and the weak/strong uniqueness. Second, using these previous results and the existence of time-periodic weak solutions proved in [B. Climent-Ezquerra, F. Guillén-González, M.A. Rojas-Medar, Reproductivity for a nematic liquid crystal model, Z. Angew. Math. Phys. 576 (6) (2006) 984–998], the regularity of any time-periodic weak solution is deduced for viscosity coefficient big enough.