  We study stable blow-up dynamics in the generalized Hartree equation with
radial symmetry, a Schr\"odinger-type equation with a nonlocal,
convolution-type nonlinearity: $iu_t+\Delta u +\left(|x|^{-(d-2)} \ast |u|^{p}
\right) |u|^{p-2}u = 0, x \in \mathbb{R}^d$. First, we consider the
$L^2$-critical case in dimensions d=3, 4, 5, 6, 7 and obtain that a generic
blow-up has a self-similar structure and exhibits not only the square root
blowup rate but also the log-log correction (via asymptotic analysis and
functional fitting). In this setting we also study blow-up profiles and show
that generic blow-up solutions converge to the rescaled $Q$, a ground state
solution of the elliptic equation $-\Delta Q+Q- \left(|x|^{-(d-2)} \ast |Q|^p
\right) |Q|^{p-2} Q =0$.
  We also consider the $L^2$-supercritical case in dimensions d=3,4. We derive
the profile equation for the self-similar blow-up and establish the existence
and local uniqueness of its solutions. As in the NLS $L^2$-supercritical
regime, the profile equation exhibits branches of non-oscillating, polynomially
decaying (multi-bump) solutions. A numerical scheme of putting constraints into
solving the corresponding ODE is applied during the process of finding the
multi-bump solutions. Direct numerical simulation of solutions to the
generalized Hartree equation by the dynamic rescaling method indicates that the
$Q_{1,0}$ is the profile for the stable blow-up. In this supercritical case, we
obtain the blow-up rate without any correction. This blow-up happens at the
focusing level $10^{-5}$, and thus, numerically observable (unlike the
$L^2$-critical case).
  In summary, we find that the results are similar to the behavior of stable
blowup dynamics in the corresponding NLS settings. Consequently, one may expect
that the form of the nonlinearity in the Schr\"odinger-type equations is not
essential in stable blow-up.
