  In this work we establish long-time existence of the normalized Yamabe flow
with positive Yamabe constant on a class of manifolds that includes spaces with
incomplete cone-edge singularities. We formulate our results axiomatically, so
that our results extend to general stratified spaces as well, provided certain
parabolic Schauder estimates hold. The central analytic tool is a parabolic
Moser iteration, which yields uniform upper and lower bounds on both the
solution and the scalar curvature.
