A catalogue of singularities
نویسندگان
چکیده
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 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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