Abstract
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 is ``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.
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