  We perform real-time hydrodynamical simulations of the growth of bubbles
formed during cosmological first-order phase transitions under the assumption
of local thermal equilibrium. We confirm that pure hydrodynamic backreaction
can lead to steady-state expansion and that bubble-wall velocity in such case
agrees very well with the analytical estimates. However, this is not the
generic outcome. Instead, it is much more common to observe runaways, as the
early-stage dynamics right after the nucleation allow the bubble walls to
achieve supersonic velocities before the heated fluid shell in front of the
bubble is formed. This effect is not captured by other methods of calculation
of the bubble-wall velocity which assume stationary solutions to exist at all
times and would have a crucial impact on the possible generation of both baryon
asymmetry and gravitational wave signals.
