  The dissipative properties of spatially nonlocal conductors are investigated
in the context of quantum friction acting on an atom moving above a macroscopic
body. The focus is on an extended version of the hydrodynamic model for the
bulk material's electromagnetic response. It is shown that the standard
hydrodynamic description is inadequate for evaluating the frictional force
since it completely neglects Landau damping. The extended version of the model
contains a frequency-dependent compressibility factor for the Fermi liquid and
qualitatively resolves this issue. For a quantitative assessment, these results
are contrasted with those obtained for the more fundamental Boltzmann-Mermin
model. Since the latter is technically involved, the simplicity of the extended
hydrodynamic model allows for an easier analysis of the impact of nonlocality
on quantum friction for other (planar) geometries. This is illustrated with an
example involving a thin slab.
