Formation of singularities for a transport equation with nonlocal velocity
Analysis of PDEs
2007-06-14 v1
Abstract
We study a 1D transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the finite time singularity is prevented and the solutions exist globally in time.
Cite
@article{arxiv.0706.1969,
title = {Formation of singularities for a transport equation with nonlocal velocity},
author = {Antonio Cordoba and Diego Cordoba and Marco A. Fontelos},
journal= {arXiv preprint arXiv:0706.1969},
year = {2007}
}
Comments
13 pages, published version