Interface dynamics in hele-shaw flows with centrifugal forces: preventing cusp singularities with rotation
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.
Magdaleno
FX
Departament d'Estructura i Constituents de la Materia, Facultat de Fisica, Universitat de Barcelona, Avenida Diagonal 647, E-08028 Barcelona, Spain.
Rocco
A
Casademunt
J