title: Singularities of the Hele-Shaw flow and shock waves in dispersive media.
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.
authors.affiliation: James Frank Institute, Enrico Fermi Institute of the University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637, USA.
authors.forename: Eldad
authors.initials: E
authors.lastname: Bettelheim
authors.forename: Oded
authors.initials: O
authors.lastname: Agam
authors.forename: Anton
authors.initials: A
authors.lastname: Zabrodin
authors.forename: Paul
authors.initials: P
authors.lastname: Wiegmann