Unstable fingering patterns of Hele-Shaw flows as a dispersionless limit of the KdV hierarchy
arXiv:cond-mat/0502179 · doi:10.1103/PhysRevLett.95.044502
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.
Published version
References in corpus (8)
- 2D Gravity and Random Matrices
- Integrable Hierarchies and Dispersionless Limit
- Integrable Structure of Interface Dynamics
- Laplacian growth as one-dimensional turbulence
- Normal random matrix ensemble as a growth problem
- Viscous fingering and a shape of an electronic droplet in the Quantum Hall regime
- A New Class of Nonsingular Exact Solutions for Laplacian Pattern Formation
- Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy
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- Matrix Models, Complex Geometry and Integrable Systems. II
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