  We study the global existence and decay to spherical equilibrium of Hele-Shaw
flows with surface tension. We prove that without injection of fluid,
perturbations of the sphere decay to zero exponentially fast. On the other
hand, with a time-dependent rate of fluid injection into the Hele-Shaw cell,
the distance from the moving boundary to an expanding sphere (with
time-dependent radius) also decays to zero but with an algebraic rate, which
depends on the injection rate of the fluid.
