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Interface dynamics in Hele-Shaw flows with centrifugal forces. Preventing cusp singularities with rotation

F. X. Magdaleno·A. Rocco·J. Casademunt
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Abstract

A class of exact solutions of Hele-Shaw flows without surface tension in a rotating cell is reported. We show that the interplay between injection and rotation modifies drastically the scenario of formation of finite-time cusp singularities. For a subclass of solutions, we show that, for any given initial condition, there exists a critical rotation rate above which cusp formation is prevented. We also find an exact sufficient condition to avoid cusps simultaneously for all initial conditions. This condition admits a simple interpretation related to the linear stability problem.

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F. X. Magdaleno, A. Rocco, J. Casademunt. 1999-10-08. Interface dynamics in Hele-Shaw flows with centrifugal forces. Preventing cusp singularities with rotation. https://doi.org/10.1103/physreve.62.r5887

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