We present a brief review of the application of boundary integral methods in two dimensions
to multicomponent fluid flows and multiphase problems in materials science. We focus on …

The classical model for studying one-phase Hele-Shaw flows is based on a highly nonlinear
moving boundary problem with the fluid velocity related to pressure gradients via a Darcy …

This monograph presents recent and new ideas arising from the study of problems of planar
fluid dynamics, and which are interesting from the point of view of geometric function theory …

One of the most influential works in fluid dynamics at the edge of the XIXth and XXth
centuries was a series of papers, see, eg,[265], written by Henry Selby Hele-Shaw between …

Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60
years ago, random matrix theory (RMT) has developed into a field of its own within applied …

We discuss the application of complex variable methods to Hele-Shaw flows and two-
dimensional Stokes flows, both with free boundaries. We outline the theory for the former, in …

From the Hele-Shaw Experiment to Integrable Systems: A Historical Overview Page 1 Compl.
anal. oper. theory 3 (2009), 551–585 c© 2008 Birkhäuser Verlag Basel/Switzerland 1661-8254/020551-35 …

We study the development of intricate, fully nonlinear immiscible interfacial patterns in the
suction-driven radial Hele-Shaw problem. The complex-shaped, contracting fluid-fluid …

We study, analytically and numerically, singularities in an interface flow driven by surface
tension and a sink in a two-dimensional Hele--Shaw cell. Our analysis proves that …

This review collates a wide variety of free boundary problems which are characterized by the
uniform proximity of the free boundary to a prescribed surface. Such situations can often be …