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

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

2005-05-11

arxiv.org/abs/nlin/0505027v3

Phys. Rev. Lett. 95, 244504 (2005)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Some typos corrected, added journal reference

Scientific paper

10.1103/PhysRevLett.95.244504

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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