Title: Critical well-posedness and scattering results for fractional Hartree-type equations,
Abstract: Scattering for the mass-critical fractional Schrödinger equation with a
cubic Hartree-type nonlinearity for initial data in a small ball in the
scale-invariant space of three-dimensional radial and square-integrable initial
data is established. For this, we prove a bilinear estimate for free solutions
and extend it to perturbations of bounded quadratic variation. This result is
shown to be sharp by proving the unboundedness of a third order derivative of
the flow map in the super-critical range.