  The generation of gravitational waves from a post-Newtonian source endowed
with a quantum spin, modeled by the Weyssenhoff fluid, is investigated in the
context of Einstein-Cartan theory at the first post-Newtonian level by
resorting to the Blanchet-Damour formalism. After having worked out the basic
principles of the hydrodynamics in Einstein-Cartan framework, we study the
Weyssenhoff fluid within the post-Newtonian approximation scheme. The
complexity of the underlying dynamical equations suggests to employ a discrete
description via the point-particle limit, a procedure which permits the
analysis of inspiralling spinning compact binaries. We then provide a first
application of our results by considering binary neutron star systems.
