Evidence of singularities for a family of contour dynamics equations.

Córdoba, Diego; Fontelos, Marco A; Mancho, Ana M; Rodrigo, Jose L · Proc Natl Acad Sci U S A · 2005

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Abstract

In this work, we show evidence of the existence of singularities developing in finite time for a class of contour dynamics equations depending on a parameter 0 < alpha </= 1. The limiting case alpha --> 0 corresponds to 2D Euler equations, and alpha = 1 corresponds to the surface quasi-geostrophic equation. The singularity is point-like, and it is approached in a self-similar manner.