  We show how to generate non-trivial solutions to the conformally invariant,
relativistic fluid dynamic equations by appealing to the Weyl covariance of the
stress tensor. We use this technique to show that a recently studied solution
of the relativistic conformally invariant Navier-Stokes equations in
four-dimensional Minkowski space can be recast as a static flow in
three-dimensional de Sitter space times a line. The simplicity of the de Sitter
form of the flow enables us to consider several generalizations of it,
including flows in other spacetime dimensions, second order viscous
corrections, and linearized perturbations. We also construct the anti-de Sitter
dual of the original four-dimensional flow. Finally, we discuss possible
applications to nuclear physics.
