  We study a 1D fluid mechanics model with nonlocal velocity. The equation can
be viewed as a fractional porous medium flow, a 1D model of the
quasi-geostrophic equation, and also a special case of Euler-Alignment system.
For strictly positive smooth initial data, global regularity has been proved by
Do, Kiselev, Ryzhik and Tan. We construct a family of non-negative smooth
initial data so that solution loses $C^1$ regularity. Our result indicates that
strict positivity is a critical condition to ensure global regularity of the
system. We also extend our construction to the corresponding models in
multi-dimensions.
