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The Hele-Shaw flow and the moduli of holomorphic discs

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  • UserJulius Ross, Cambridge
  • ClockWednesday 30 January 2013, 16:00-17:00
  • HouseMR13.

If you have a question about this talk, please contact Ivan Smith.

The Hele-Shaw Flow is a model for describing the propagation of fluid in a cell consisting of two parallel plates separated by a small gap. This model has been intensely studied for over a century, and is a paradigm for understanding more complicated systems such as the flow of water in porous media, melting of ice and models of tumor growth.

In this talk I will discuss how this flow fits into the more general framework of “inverse potential theory” through the idea of complex moments. I will then discuss joint work with David Witt Nystrom that connects to the moduli space of holomorphic discs with boundary in a totally real manifold. Using this we prove a number of short time existence/uniqueness results for the flow, including the case of the Hele Shaw flow with varying permeability starting from a smooth Jordan domain, and for the Hele Shaw flow starting from a single point.

This talk is part of the Differential Geometry and Topology Seminar series.

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