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The Euler-Poisson (EP) system describes the dynamic behavior of manyimportant physical flows. In this work, a Riccati system that governstwo-dimensional EP equations is studied. The evolution of divergence isgoverned by the Riccati type equation with several nonlinear/nonlocal terms.Among these, the vorticity accelerates divergence while others further amplifythe blow-up behavior of a flow. The growth of these blow-up amplifying termsare related to the Riesz transform of density, which lacks a uniform boundmakes it difficult to study global solutions of the multi-dimensional EPsystem. We show that the Riccati system can afford to have global solutions, aslong as the growth rate of blow-up amplifying terms is not higher thanexponential, and admits global smooth solutions for a large set of initialconfigurations. To show this, we construct an auxiliary system in 3D space andfind an invariant space of the system, then comparison with the original 2Dsystem is performed. Some numerical examples are also presented.

On the Riccati dynamics of 2D Euler-Poisson equations with attractive forcing