On the Riccati dynamics of the Euler-Poisson equations with zero background state

TL;DR

This paper analyzes the Riccati system governing the gradient dynamics of the 2D Euler-Poisson equations with attractive or repulsive forces, demonstrating conditions for global smooth solutions for many initial states.

Contribution

It extends previous work by identifying conditions under which the Euler-Poisson system admits global smooth solutions based on Riccati dynamics.

Findings

Global smooth solutions exist under certain conditions

Applicable to systems with both attractive and repulsive forces

Builds on previous research to broaden understanding

Abstract

This paper studies the two-dimensional Euler-Poisson equations associated with either attractive or repulsive forces. We mainly study the Riccati system that governs the flow's gradient. Under a suitable condition, it is shown that the Euler-Poisson system admits global smooth solutions for a large set of initial configurations. This paper is a continuation of our former work [8].