In this talk, I will describe some recent results on analytic aspects of both equilibrium solutions and hydrodynamics of a simplified model of biaxial nematic liquid crystals proposed by Govers, Vertogen, and Leslie 1980’s, which is represented by a pair of orthogonal unit-vector fields. This model is an extension of the Oseen-Frank theory, which can be reduced from the Landau-De Gennes Q-tensor theory. We will discuss a partial regularity theorem for equilibrium solutions, and the existence of a unique global weak solution of the hydrodynamic equation in dimension two for such a model. This is a joint work with Junyu Lin.