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 time-independent Dirichlet bound- ary conditions are imposed for the orientation of crystal molecules. Neverthe- less, for the time-dependent case, the treatment of the problem is completely di erent. The veri cation of a maximum principle for weak reproductive so- lutions is fundamental in the argument. Finally, the relation between reproductive and periodic in time (regular) solutions will be pointed out, di erenting the 2D and 3D cases. Basically, in two-dimensional domains every reproductive solution is regular and time periodic, whereas the problem remains open for three-dimensional domains.