  We investigate the Cauchy problem for the Vlasov--Riesz system, which is a
Vlasov equation featuring an interaction potential generalizing previously
studied cases, including the Coulomb $\Phi = (-\Delta)^{-1}\rho$, Manev
$(-\Delta)^{-1} + (-\Delta)^{-\frac12}$, and pure Manev $(-\Delta)^{-\frac12}$
potentials. For the first time, we extend the local theory of classical
solutions to potentials more singular than that for the Manev. Then, we obtain
finite-time singularity formation for solutions with various attractive
interaction potentials, extending the well-known blow-up result of Horst for
attractive Vlasov--Poisson for $d\ge4$. Our local well-posedness and
singularity formation results extend to cases when linear diffusion and damping
in velocity are present.
