The expansion and chemical equilibration of a quark-gluon plasma formed in collisions of two heavy nuclei may be described by relativistic fluid dynamics, in combination with chemical rate equations for the different parton species. Using initial conditions obtained from a self-screened parton cascade calculation and allowing for the full three-dimensional expansion of the parton plasma, we make predictions about the life-time of the quark-gluon plasma and the transverse flow velocity at hadronization for Au + Au collisions at RHIC and LHC energy.