title: Unstable fingering patterns of Hele-Shaw flows as a dispersionless limit of the Kortweg-de vries hierarchy.
abstract: We show that unstable fingering patterns of two-dimensional flows of viscous fluids with open boundary are described by a dispersionless limit of the Korteweg-de Vries hierarchy. In this framework, the fingering instability is linked to a known instability leading to regularized shock solutions for nonlinear waves, in dispersive media. The integrable structure of the flow suggests a dispersive regularization of the finite-time singularities.
authors.affiliation: Physics Department, Columbia University, New York, New York 10027, USA.
authors.forename: Razvan
authors.initials: R
authors.lastname: Teodorescu
authors.forename: Paul
authors.initials: P
authors.lastname: Wiegmann
authors.forename: Anton
authors.initials: A
authors.lastname: Zabrodin