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On nonlinear interface dynamics in Hele-Shaw flows

1995; Cambridge University Press; Volume: 6; Issue: 5 Linguagem: Inglês

10.1017/s0956792500001959

1469-4425

V. M. Entov, Pavel Etingof, Dmitry Kleinbock,

Complex Systems and Time Series Analysis

Flows with free boundaries in a Hele-Shaw cell provide a unique opportunity to study non-linear boundary dynamics using rigorous analytic approaches. While of limited direct ‘practical value’, these studies give rise to a plethora of new phenomena and insights which may serve as beacons in the turbulent ocean of moving free boundaries and pattern forming. This paper gives a brief summary of the authors' studies of Hele-Shaw flows with free boundaries and some related problems based upon Richardson's approach. Some promising directions of further research are also discussed.