The dynamical appearance of scaling solutions in relativistic hydrodynamics is studied for boost-invariant, cylindrically symmetric systems. Such solutions reproduce key qualitative features of the blast-wave, Buda-Lund, and Cracow models, which in turn fit a broad set of data measured in ultrarelativistic heavy-ion collisions. Effects of a phase transition are taken into account by using a temperature-dependent speed of sound, inferred from a lattice QCD equation of state. The transverse flow may acquire the asymptotic Hubble form $r/t$ within short evolution times, 7--15 fm, only if an initial pre-equilibrium transverse flow is present. The precise amount of the requisite pre-equilibrium flow is anticorrelated with the initial value of the central temperature.
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Chojnacki et al. (2005) studied this question.