  We study the role of viscosity and the effects of a magnetic field on a
rotating, self-gravitating fluid, using Newtonian theory and adopting the ideal
magnetohydrodynamic approximation. Our results confirm that viscosity can
generate vorticity in inhomogeneous environments, while the magnetic tension
can produce vorticity even in the absence of fluid pressure and density
gradients. Linearizing our equations around an Einstein-de Sitter cosmology, we
find that viscosity adds to the diluting effect of the universal expansion.
Typically, however, the dissipative viscous effects are confined to relatively
small scales. We also identify the characteristic length bellow which the
viscous dissipation is strong and beyond which viscosity is essentially
negligible. In contrast, magnetism seems to favor cosmic rotation. The magnetic
presence is found to slow down the standard decay-rate of linear vortices, thus
leading to universes with more residual rotation than generally anticipated.
