Remarks on global existence of classical solution to multi-dimensional compressible Euler-Poisson equations with geometrical symmetry

TL;DR

This paper establishes a precise criterion for the global existence of classical solutions to multi-dimensional compressible Euler-Poisson equations with radial symmetry, based on initial conditions and force balance.

Contribution

It introduces a new quantity that captures the interplay between initial velocity and Poisson force strength, providing necessary and sufficient conditions for solution existence.

Findings

Derived a necessary and sufficient condition for global solutions

Introduced a new measure for initial velocity and force balance

Clarified the role of geometrical symmetry in solution behavior

Abstract

We give a necessary and sufficient condition for the global existence of the classical solution to the Cauchy problem of the compressible Euler-Poisson equations with radial symmetry. We introduce a new quantity which describes the balance between the initial velocity of the flow and the strength of the force governed by Poisson equation.