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math.AP2007
A catalogue of singularities
Jens Eggers, Marco A. Fontelos
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 co…
math.AP2007
Formation of singularities for a transport equation with nonlocal velocity
Antonio Cordoba, Diego Cordoba, Marco A. Fontelos
We study a 1D transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the…