Cusp formation for a nonlocal evolution equation
Analysis of PDEs
2017-02-17 v2
Abstract
In this paper, we introduce a nonlocal evolution equation inspired by the C\'ordoba-C\'ordoba-Fontelos nonlocal transport equation. The C\'ordoba-C\'ordoba-Fontelos equation can be regarded as a model for the 2D surface quasigeostrophic equation or the Birkhoff-Rott equation. We prove blowup in finite time, and more importantly, investigate conditions under which the solution forms a cusp in finite time.
Cite
@article{arxiv.1602.02451,
title = {Cusp formation for a nonlocal evolution equation},
author = {Vu Hoang and Maria Radosz},
journal= {arXiv preprint arXiv:1602.02451},
year = {2017}
}
Comments
15 pages, 2 figures