We prove that every 3-manifold possesses a C1, volume-preserving flow with
no fixed points and no closed trajectories. The main construction is a
volume-preserving version of the Schweitzer plug. We also prove that every
3-manifold possesses a volume-preserving, Cβ flow with discrete closed
trajectories and no fixed points (as well as a PL flow with the same geometry),
which is needed for the first result. The proof uses a Dehn-twisted Wilson-type
plug which also preserves volume