Abstract:
 This talk addresses a largetime rescaling behavior of HeleShaw cells for large data initial domains. The PolubarinovaGalin equation is the reformulation of zero surface tension HeleShaw ows with injection at the origin in two dimensions by considering the moving domain $\Omega(t) = f(B_1(0),t)$ for some Riemann mapping $f(\xi,t)$. We give a sharp
largetime rescaling behavior of global strong polynomial solutions to this equation and hence obtain a sharp rescaling behavior of the moving domains. Furthermore, we also show that a small perturbation of the initial function of a global strong polynomial solution also gives rise to a global strong solution and a largetime rescaling behavior of the moving domain is shown as well.
