Reproductivity for a Nematic Liquid Crystal Model

In this paper we prove existence of weak solution with the reproductivity in time property, for a penalized PDE's system related to a nematic liquid crystal model. This problem is relatively explicit when time­independent Dirichlet boundary conditions are imposed for the orientation of crystal molecules. For the time­dependent case, the verification of a maximum principle for weak reproductive solutions is fundamental in the argument. Finally, the relation between reproductive and periodic in time solutions and their dependence respect to the regularity will be pointed out, being completely different the 2D and 3D cases.