  We consider here an elliptic coupled system describing the dynamics of liquid
crystals flows. This system is posed on the whole n-dimensional space. We
introduce first the notion of very weak solutions for this system. Then, within
the fairly general framework of the Morrey spaces, we derive some sufficient
conditions on the very weak solutions which improve their regularity. As a
bi-product, we also prove a new regularity criterium for the time-independing
Navier-Stokes equations.
