  A general relativistic version of the Euler equation for perfect fluid
hydrodynamics is applied to a system of two neutron stars orbiting each other.
In the quasi-equilibrium phase of the evolution of this system, a first
integral of motion can be derived for certain velocity fields of the neutron
star fluid including the (academic) case of co-rotation with respect to the
orbital motion (synchronized binaries) and the realistic case of
counter-rotation with respect to the orbital motion. The velocity field leading
to this latter configuration can be computed by solving three-dimensional
vector and scalar Poisson equations.
