Global existence and regularity of solutions for active liquid crystals

We study the hydrodynamics of active liquid crystals in the Beris–Edwards hydrodynamic framework with the Landau–de Gennes Q-tensor order parameter to describe liquid crystalline ordering. The existence of global weak solutions in two and three spatial dimensions is established. In the two-dimensional case, by the Littlewood–Paley decomposition, the higher regularity of the weak solutions and the weak-strong uniqueness are also obtained.