A catalogue of singularities

Jens Eggers; Marco A. Fontelos

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arXiv · 0711.0442

A catalogue of singularities

Jens Eggers·Marco A. Fontelos

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Abstract

This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and where typical scales of the solution shrink to zero as the singularity is approached. Upon a similarity transformation, exact self-similar behaviour is mapped to the fixed point of a {\it infinite dimensional dynamical system} representing the original dynamics. We show that the dynamics close to the fixed point is a useful way classifying the structure of the singularity. Specifically, we consider various types of stable and unstable fixed points, centre-manifold dynamics, limit cycles, and chaotic dynamics.

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Jens Eggers, Marco A. Fontelos. 2007-11-03. A catalogue of singularities. https://arxiv.org/abs/0711.0442

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