Evidence of singularities for a family of contour dynamics equations.
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.
Córdoba
Diego
D
Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, C/Serrano 123, Madrid 28006, Spain. dcg@imaff.cfmac.csic.es
Fontelos
Marco A
MA
Mancho
Ana M
AM
Rodrigo
Jose L
JL