  [Background] Experimental data from heavy-ion experiments at RHIC-BNL and
LHC-CERN are quantitatively described using relativistic fluid dynamics. Even
p+A and p+p collisions show signs of collective behavior describable in the
same manner. Nevertheless, small system sizes and large gradients strain the
limits of applicability of fluid-dynamical methods. [Purpose] The range of
applicability of fluid dynamics for the description of the collective behavior,
and in particular of the elliptic flow, of small systems needs to be explored.
[Method] Results of relativistic fluid-dynamical simulations are compared with
solutions of the Boltzmann equation in a longitudinally boost-invariant
picture. As initial condition, several different transverse energy-density
profiles for equilibrated matter are investigated. [Results] While there is
overall a fair agreement of energy- and particle-density profiles, components
of the shear-stress tensor are more sensitive to details of the implementation.
The highest sensitivity is exhibited by quantities influenced by properties of
the medium at freeze-out. [Conclusions] For some quantities, like the
shear-stress tensor, agreement between fluid dynamics and transport theory
extends into regions of Knudsen numbers and inverse Reynolds numbers where
relativistic fluid dynamics is believed to fail.
