  The description of a stellar system as a continuous fluid represents a
convenient first approximation to stellar dynamics, and its derivation from the
kinetic theory is standard. The challenge lies in providing adequate closure
approximations for the higher-order moments of the phase-space density function
that appear in the fluid dynamical equations. Such closure approximations may
be found using representations of the phase-space density as embodied in the
kinetic theory. In the classic approach of Chapman and Enskog, one is led to
the Navier-Stokes equations, which are known to be inaccurate when the mean
free paths of particles are long, as they are in many stellar systems. To
improve on the fluid description, we derive here a modified closure relation
using a Fokker-Planck collision operator. To illustrate the nature of our
approximation, we apply it to the study of gravitational instability. The
instability proceeds in a qualitative manner as given by the Navier-Stokes
equations but, in our description, the damped modes are considerably closer to
marginality, especially at small scales.
