Numerical study of a flow of regular planar curves that develop singularities at finite time
Numerical Analysis
2008-12-08 v1 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.0812.1153,
title = {Numerical study of a flow of regular planar curves that develop singularities at finite time},
author = {Francisco de la Hoz},
journal= {arXiv preprint arXiv:0812.1153},
year = {2008}
}