LAUSR

Abstract We consider the incompressible flow of the active hydrodynamics of liquid crystals with inhomogeneous density in the Beris-Edwards hydrodynamics framework. The Landau-de Gennes Q-tensor order parameter is used to describe the liquid crystalline ordering. Faedo-Galerkin's method is adopted to construct the solutions for the initial-boundary value problem. Two levels of approximations are used and the weak convergence is obtained through compactness estimates by new techniques due to the active terms. The existence of global weak solutions in dimension two and three is established in a bounded domain.