Singular limit of Hele-Shaw flow and dispersive regularization of shock waves
Exactly Solvable and Integrable Systems
2007-05-23 v3 Soft Condensed Matter
Pattern Formation and Solitons
Fluid Dynamics
Abstract
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 of an isolated finger is given by the Whitham equations for the KdV integrable hierarchy. We show that the flow describing bubble break-off is identical to the Gurevich-Pitaevsky solution for regularization of shock waves in dispersive media. The method provides a scheme for the continuation of the flow through singularites.
Keywords
Cite
@article{arxiv.nlin/0505027,
title = {Singular limit of Hele-Shaw flow and dispersive regularization of shock waves},
author = {Eldad Bettelheim and Oded Agam and Anton Zabrodin and Paul Wiegmann},
journal= {arXiv preprint arXiv:nlin/0505027},
year = {2007}
}
Comments
Some typos corrected, added journal reference