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

R. Teodorescu; A. Zabrodin; P. Wiegmann

doi:10.1103/physrevlett.95.044502

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

R. Teodorescu·A. Zabrodin·P. Wiegmann

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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 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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R. Teodorescu, A. Zabrodin, P. Wiegmann. 2006-09-27. Unstable fingering patterns of Hele-Shaw flows as a dispersionless limit of the KdV hierarchy. https://doi.org/10.1103/physrevlett.95.044502

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