  Predictivity of the Kohn-Sham approach to dynamical problems, when regarded
as an initial value problem in a time-dependent density functional framework,
is analysed for a class of models for which the argument devised in the work of
Maitra et al. (Phys. Rev. A 78, 056501 (2008), arXiv:cond-mat/0710.0018) for
the standard electronic many-body problem does not apply. The original argument
is here extended and revised. As a result, predictivity for this class of
problems seems possible only at the price of introducing extra unknown
functionals in the corresponding Kohn-Sham equation. Furthermore, the same
argument, when applied to original electronic problem, suggests that the
Hartree-exchange-correlation potential is not unambiguously identified by the
contemporary and past densities and initial states, but also requires knowledge
of the divergence of the contemporary Kohn-Sham current.
