  The correlations of the fluctuating stress tensor are calculated in an
equilibrium molecular-dynamics simulation of a Lennard--Jones liquid. We define
a coarse-grained local stress tensor which can be calculated numerically and
which allows for the first time to determine the stress correlation function
both in time and in space. Our findings corroborate the assumptions made in
fluctuating hydrodynamics as long as the liquid is isotropic, that is in bulk.
In the vicinity of a rigid plate, however, the isotropy is restricted, and
major modifications must be done with respect to the usual theory. Among these
are the appearance of five different viscosities instead of two and a
non-trivial dependence of the distance from the wall. We determine these
viscosities from the simulation data and find that their values are very
different from the bulk values. We further find much longer relaxation times of
the stress correlations than in bulk.
