Extraordinary Analysis Group Seminar on Monday

Speaker: Dr. Yu-Lin Lin (Institute of Mathematics, Academia Sinica, Taipei, Taiwan)

Title: "Large-time rescaling behaviors to the Hele-Shaw problem driven by injection"

Abstract: This talk addresses a large-time rescaling behavior of Hele-Shaw cells for large  data initial domains. The Polubarinova-Galin equation is the reformulation of zero surface tension Hele-Shaw flows 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(z,t). We give a sharp large-time rescaling behavior of global strong polynomial solutions to this equation and the corresponding moving boundary in terms of the invariant complex moments. Furthermore, by proving a perturbation theorem of polynomial solutions, we also show that a small perturbation of the initial function of a global strong polynomial solution also gives rise to global strong solution and a large-time rescaling behavior of the  moving domain is shown as well.

Information on previous seminars can be found here.