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