  We consider two elliptic coupled systems of relevance in the fluid dynamics.
These systems are posed on the whole three-dimensional space and they consider
the action of external forces. The first system deals with the simplified
Ericksen-Leslie (SEL) system, which describes the dynamics of liquid crystal
flows. The second system is the time-independent magneto-hydrodynamic (MHD)
equations. For the (SEL) system, we obtain a new criterion to improve the
regularity of weak solutions, provided that they belong to some homogeneous
Morrey space. As a bi-product, we also obtain some new regularity criterion for
the stationary Navier-Stokes equations and for a nonlinear harmonic map flow.
This new regularity criterion also holds true for the (MHD) equations.
Furthermore, for this last system we are able to use the Gevrey class to prove
that all finite energy weak solutions are analytic functions, provided the
external forces belong to some Gevrey class.
