In this talk I’ll present my master’s thesis project, focused on the Beris-Edward model. This system studies the behaviour of a molecule in a flux of nematic liquid crystals, a state of matter intermediate between the solid state and the liquid one. We consider the case with absence of flow and with energy functional unbounded from below. At the beginning, we study the stationary problem. We prove the existence of a least energy solution (when the domain is all the space) and of ground states with several open sets and boundary conditions. The last part is devoted to the evolution problem in all the space, where we establish local and global existence with small initial data. The results come from several applications of Strichartz-type estimates and by contraction arguments.