Regularity of weak solutions for the stationary Ericksen–Leslie and MHD systems

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