  We present hydrodynamic equations with relativistic pressure and velocity in
the presence of weak gravity, in a cosmological context. Previously we
consistently derived special relativistic hydrodynamic equations with weak
gravity in Minkowski background. With the relativistic pressure and velocity
one cannot derive the cosmological counterpart by a simple transformation from
equations in the Minkowski background. Here we present a proper derivation. We
point out the potential importance of relativistic pressure and velocity in
gravitational lensing.
