Cusp formation for a nonlocal evolution equation

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.