Recently Navier-Stokes (NS) equations have been derived from the duality
between the black branes and a conformal fluid on the boundary of AdS_5.
Nevertheless, the full correspondence has to be established between solutions
of supergravity in AdS_5 and supersymmetric field theories on the boundary.
That prompts the construction of NS equations for a supersymmetric fluid. In
the framework of rigid susy, there are several possibilities and we propose one
candidate. We deduce the equations of motion in two ways: both from the
divergenless condition on the energy-momentum tensor and by a suitable
parametrization of the auxiliary fields. We give the complete component
expansion and a very preliminary analysis of the physics of this supersymmetric
fluid.Comment: 24 pages, Latex2
