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

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

2005-02-07

arxiv.org/abs/cond-mat/0502179v4

Phys.Rev.Lett. 95 (2005) 044502

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Published version

Scientific paper

10.1103/PhysRevLett.95.044502

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.

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