English

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

R2 v1 2026-06-22T12:45:08.661Z