Cusp formation for a nonlocal evolution equation
arXiv:1602.02451 · doi:10.1007/s00205-017-1094-3
Abstract
In this paper, we introduce a nonlocal evolution equation inspired by the Córdoba-Córdoba-Fontelos nonlocal transport equation. The Córdoba-Córdoba-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.
15 pages, 2 figures