  Looking for the underlying hydrodynamic mechanisms determining the elliptic
flow we show that for an expanding relativistic perfect fluid the transverse
flow may derive from a solvable hydrodynamic potential, if the entropy is
transversally conserved and the corresponding expansion "quasi-stationary",
that is mainly governed by the temperature cooling. Exact solutions for the
velocity flow coefficients $v_2$ and the temperature dependence of the spatial
and momentum anisotropy are obtained and shown to be in agreement with the
elliptic flow features of heavy-ion collisions.
