  We consider a parabolic-type PDE with a diffusion given by a fractional
Laplacian operator and with a quadratic nonlinearity of the 'gradient' of the
solution, convoluted with a singular term b. Our first result is the
well-posedness for this problem: We show existence and uniqueness of a (local
in time) mild solution. The main result is about blow-up of said solution, and
in particular we find sufficient conditions on the initial datum and on the
term b to ensure blow-up of the solution in finite time.
