A time dependent coupled system related to the tridimensional equations of a nematic liquid crystal

In this paper we prove some results about the existence, uniqueness and regularity of the solutions of a tridimensional variational approximated model for the Leslie's equations of an incompressible nematic liquid crystal (cf. 7]). This model was introduced in 1] where the bidimensional case is studied. Here we use the methods developed in 6], 4] and 8].