270 citations · 1.7k across the 38 of their papers we have counts for
6 papers · 1 filter
Viscous shocks in Hele-Shaw flow and Stokes phenomena of the Painleve I transcendent
Seung-Yeop Lee, Razvan Teodorescu, Paul Wiegmann
In Hele-Shaw flows at vanishing surface tension, the boundary of a viscous fluid develops cusp-like singularities. In recent papers [1, 2] we have showed that singularities trigger…
Shocks and finite-time singularities in Hele-Shaw flow
Seung-Yeop Lee, Razvan Teodorescu, Paul Wiegmann
Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusp-like singularities. We show that the ill-defined problem admits a weak {\it dispe…
Bubble break-off in Hele-Shaw flows : Singularities and integrable structures
Seung-Yeop Lee, Eldad Bettelheim, Paul Wiegmann
Bubbles of inviscid fluid surrounded by a viscous fluid in a Hele-Shaw cell can merge and break-off. During the process of break-off, a thinning neck pinches off to a universal sel…
Singular limit of Hele-Shaw flow and dispersive regularization of shock waves
Eldad Bettelheim, Oded Agam, Anton Zabrodin +1
We study a family of solutions to the Saffman-Taylor problem with zero surface tension at a critical regime. In this regime, the interface develops a thin singular finger. The flow…
Laplacian Growth and Whitham Equations of Soliton Theory
I. Krichever, M. Mineev-Weinstein, P. Wiegmann +1
The Laplacian growth (the Hele-Shaw problem) of multi-connected domains in the case of zero surface tension is proven to be equivalent to an integrable systems of Whitham equations…
Integrable Structure of Interface Dynamics
Mark Mineev-Weinstein, Paul B. Wiegmann, Anton Zabrodin
We establish the equivalence of a 2D contour dynamics to the dispersionless limit of the integrable Toda hierarchy constrained by a string equation. Remarkably, the same hierarchy…