Eulerian perturbation theory in non-flat universes: second-order approximation

The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity potentials: the problem can be afforded {\it exactly}, rather than approximately, even for cosmological models with arbitrary density parameter \Omega. The Eulerian approach we present here allows to calculate the higher-order moments of the initially Gaussian density and velocity fields: in particular, we compute the gravitationally induced skewness of the density and velocity-divergence fields for any value of \Omega, showing that the \Omega-dependence of the skewness is extremely weak. This fact, though qualitatively confirming previous results obtained via Lagrangian perturbation theory, specifies the correct \Omega-dependence and restricts the reliability of the separability assumption of higher-order perturbative solutions to the Einstein-de Sitter case only