  The main goal of this paper is to give a precise description of rescaling
behaviors of rational type global strong solutions to the Polubarinova-Galin
equation. The Polubarinova-Galin equation is the reformulation of the zero
surface tension Hele-Shaw problem with a single source at the origin by
considering the moving domain as the Riemann mapping of the unit disk centered
at the origin. The coefficients $\{a_{k}(t)\}_{k\geq 2}$ of the polynomial
strong solution $f_{k_{0}}(\xi,t)=\sum_{i=1}^{k_{0}}a_{i}(t)\xi^{i}$ decay to
zero algebraically as $t^{-\lambda_{k}}$ ($\lambda_{k}=k/2$) and the decay is
even faster if the low Richardson moments vanish. The dynamics for global
solutions are discussed as well.
