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Published on: February 3, 2014
Singularities of the Hele-Shaw flow and shock waves in dispersive media
Eldad Bettelheim1, Oded Agam, Anton Zabrodin
1James Frank Institute, Enrico Fermi Institute of the University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA.
Abstract:
We show that singularities developed in the Hele-Shaw problem have a structure identical to shock waves in dissipativeless dispersive media. We propose an experimental setup where the cell is permeable to a nonviscous fluid and study continuation of the flow through singularities. We show that a singular flow in this nontraditional cell is described by the Whitham equations identical to Gurevich-Pitaevski solution for a regularization of shock waves in Korteveg-de Vriez equation. This solution describes regularization of singularities through creation of disconnected bubbles.
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