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Singular limit of Hele-Shaw flow and dispersive regularization of shock waves

Eldad Bettelheim·Oded Agam·Anton Zabrodin·Paul Wiegmann
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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.

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Eldad Bettelheim, Oded Agam, Anton Zabrodin, Paul Wiegmann. 2006-05-03. Singular limit of Hele-Shaw flow and dispersive regularization of shock waves. https://doi.org/10.1103/physrevlett.95.244504

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