Long-pin perturbations of the trivial solution for Hele-Shawcorner flows

Abstract

We consider two-dimensional Hele-Shaw corner flows without effect of the surface tension and with an interface extending to the infinity along one of the walls. Explicit solutions that present a ”long-pin” deformations of the trivial solution are got. Making use of the Polubarinova-Galin approach we derive parametric equations for the moving interface in terms of univalent mappings of a canonical domain. For the right angle we repeat a result by Leo P. Kadanoff.