  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.
