%0 Journal Article
%T Numerical study of a flow of regular planar curves that develop singularities at finite time
%A Francisco de la Hoz
%J Mathematics
%D 2008
%I arXiv
%X In this paper, we will study the following geometric flow, obtained by Goldstein and Petrich while considering the evolution of a vortex patch in the plane under Euler's equations, X_t = -k_s n - (1/2) k^2 T, with s being the arc-length parameter and k the curvature. Perelman and Vega proved that this flow has a one-parameter family of regular solutions that develop a corner-shaped singularity at finite time. We will give a method to reproduce numerically the evolution of those solutions, as well as the formation of the corner, showing several properties associated to them.
%U http://arxiv.org/abs/0812.1153v1