Surprises in Viscous Fingering

Saleh Tanveer
Department of Mathematics
Ohio State

Abstract: The displacement of a viscous fluid by a less viscous fluid in a Hele-Shaw cell has been an active area of research for many years. In this talk, some apparently surprising results for steady and unsteady fingering both from mathematical and physical aspects will be presented. These include role of exponential asymptotics, structural instability as well as singular perturbation for an initial value problem.