7 citations · 14 across the 8 of their papers we have counts for
8 papers
Non-univalent solutions of the Polubarinova-Galin equation
Björn Gustafsson, Yu-Lin Lin
We study non-univalent solutions of the Polubarinova-Galin equation, describing the time evolution of the conformal map from the unit disk onto a Hele-Shaw blob of fluid subject to…
Classification of degree three polynomial solutions to the Polubarinova-Galin equation
Yu-Lin Lin
The Polubarinova-Galin equation is derived from zero-surface-tension Hele-Shaw flow driven by injection. In this paper, we classify degree three polynomial solutions to the Polubar…
On the dynamics of roots and poles for solutions of the Polubarinova-Galin equation
Björn Gustafsson, Yu-Lin Lin
We study the dynamics of roots of f'(z,t), where f(z,t) is a locally univalent polynomial solution of the Polubarinova-Galin equation for the evolution of the conformal map onto a…
Perturbation theorems for Hele-Shaw flows and their applications
Yu-Lin Lin
In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw equation driven by injection or suction, so called the Polubarino…
Large-time rescaling behaviors of Stokes and Hele-Shaw flows driven by injection
Yu-Lin Lin
In this paper, we give a precise description of the rescaling behaviors of global strong polynomial solutions to the reformulation of zero surface tension Hele-Shaw problem driven…
Existence and uniqueness of the Hele-Shaw problem with injection
Yulin Lin
This paper gives a new and short proof of existence and uniqueness of the Polubarinova-Galin equation. The existence proof is an application of the main theorem in Lin's paper. Fur…
Large-time rescaling behaviors for large data to the Hele-Shaw problem
Yulin Lin
This paper addresses a rescaling behavior of some classes of global solutions to the zero surface tension Hele-Shaw problem with injection at the origin, . Here…
Large-time rescaling behaviors of some rational type solutions to the Polubarinova-Galin equation with injection
Yulin Lin
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-Ga…