The two models we are considering in this work relate to the Navier-Stokes equations, which describe the motion of a viscous fluid. The first of these two models is the Beris–Edwards model of nematic liquid crystals, which couples the Navier-Stokes equations with a parabolic equation for the molecular orientation described by the Q-tensor. The second topic we are investigating is the primitive equations equations for atmospheric and oceanic flows, which are derived from the Navier–Stokes equations by the hydrostatic approximation.