Recent analytic results concerning stationary, self-gravitating fluids in
Newtonian theory are discussed. We give a theorem that forbids infinitely
extended fluids, depending on the assumed equation of state and the rotation
law. This part extends previous results that have been obtained for static
configurations. The second part discusses a Sobolev bound on the mass of the
fluid and a rigorous Jeans-type inequality that is valid in the stationary
case.Comment: A talk given at the Spanish Relativity Meeting in Portugal 2012. To
appear in Progress in Mathematical Relativity, Gravitation and Cosmology,
Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho,
Guimaraes, Portugal, 3-7 September 2012, Springer Proceedings in Mathematics
& Statistics, Vol. 6
