Numerical study of a flow of regular planar curves that develop singularities at finite time

Details Numerical study of a flow of regular planar curves that develop singularities at finite time Numerical study of a flow of regular planar curves that develop singularities at finite time

2008-12-05

arxiv.org/abs/0812.1153v1

Mathematics

Numerical Analysis

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Numerical study of a flow of regular planar curves that develop singularities at finite time does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Numerical study of a flow of regular planar curves that develop singularities at finite time, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Numerical study of a flow of regular planar curves that develop singularities at finite time will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-365848