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

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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 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 suppressed. We also find an exact sufficient condition to avoid cusps simultaneously for all initial conditions within the above subclass.

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MAGDALENO ESCAR, Francesc Xavier, ROCCO, Andrea and CASADEMUNT I VIADER, Jaume. Interface dynamics in Hele-Shaw flows with centrifugal forces. Preventing cusp singularities with rotation. Physical Review E. 2000. Vol. 62, num. 5, pags. R5887-R5890. ISSN 0031-9007. [consulted: 1 of July of 2026]. Available at: https://hdl.handle.net/2445/18763

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