  Recent discussions of RHIC data emphasized the exciting possibility that the
matter produced in nucleus-nucleus collisions shows properties of a
near-perfect fluid. Here, we aim at delineating the applicability of fluid
dynamics, which is needed to quantify the size of corresponding dissipative
effects. We start from the equations for dissipative fluid dynamics, which we
derive from kinetic theory up to second order (Israel-Stewart theory) in a
systematic gradient expansion. In model studies, we then establish that for too
early initialization of the hydrodynamic evolution ($\tau_0 \lsim 1$ fm/c) or
for too high transverse momentum ($p_T \gsim 1$ GeV) in the final state, the
expected dissipative corrections are too large for a fluid description to be
reliable. Moreover, viscosity-induced modifications of hadronic transverse
momentum spectra can be accommodated to a significant degree in an ideal fluid
description by modifications of the decoupling stage. We argue that these
conclusions, drawn from model studies, can also be expected to arise in
significantly more complex, realistic fluid dynamics simulations of heavy ion
collisions.
