Unstable fingering patterns of Hele-Shaw flows as a dispersionless limit of the KdV hierarchy

Teodorescu, R.; Zabrodin, A.; Wiegmann, P.

Unstable fingering patterns of Hele-Shaw flows as a dispersionless limit of the KdV hierarchy

Authors

Teodorescu, R.

Zabrodin, A.

Wiegmann, P.

Description

We show that unstable fingering patterns of two dimensional flows of viscous fluids with open boundary are described by a dispersionless limit of the KdV 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.
Published version